300 (number)

{{Infobox number | number = 300 | lang1 = Hebrew | lang1 symbol = ש |lang2=Armenian|lang2 symbol=Յ|lang3=Babylonian cuneiform|lang3 symbol=𒐙|lang4=Egyptian hieroglyph|lang4 symbol=𓍤}}

'''300''' ('''three hundred''') is the natural number following 299 and preceding 301. {{TOC limit|3}}

== In mathematics == 300 is a composite number and the 24th triangular number.<ref>{{Cite web |title=A000217 - OEIS |url=https://oeis.org/A000217 |access-date=2024-11-28 |website=oeis.org}}</ref> It is also a second hexagonal number.<ref>{{Cite OEIS|A014105|second hexagonal number}}</ref>

== Integers from 301 to 399 ==

=== 300s ===

==== 301 ==== {{Main|301 (number)}}

==== 302 ==== {{Main|302 (number)}}

==== 303 ==== {{Main|303 (number)}}

==== 304 ==== {{main|304 (number)}}

==== 305 ==== {{Main|305 (number)}}

==== 306 ==== {{Main|306 (number)}}

==== 307 ==== {{Main|307 (number)}}

==== 308 ==== {{Main|308 (number)}}

==== 309 ==== {{Main|309 (number)}}

=== 310s ===

==== 310 ==== {{Main|310 (number)}}

==== 311 ==== {{Main|311 (number)}}

==== 312 ==== {{Main|312 (number)}}

==== 313 ==== {{Main|313 (number)}}

==== 314 ==== {{Main|314 (number)}}

==== 315 ==== {{main|315 (number)}}

==== 316 ==== {{Main|316 (number)}} 316 = 22 × 79, a centered triangular number<ref name="A005448">{{Cite OEIS|A005448|Centered triangular numbers}}</ref> and a centered heptagonal number.<ref name="A069099">{{Cite OEIS|A069099|Centered heptagonal numbers}}</ref>

==== 317 ====

317 is a prime number, Eisenstein prime with no imaginary part, Chen prime,<ref name=A109611>{{Cite OEIS|A109611|Chen primes}}</ref> one of the rare primes to be both right and left-truncatable,<ref name=A020994>{{Cite OEIS|A020994|Primes that are both left-truncatable and right-truncatable}}</ref> and a strictly non-palindromic number.

317 is the exponent (and number of ones) in the fourth base-10 repunit prime.<ref>Guy, Richard; ''Unsolved Problems in Number Theory'', p. 7 {{ISBN|1475717385}}</ref>

==== 318 ====

==== 319 ====

319 = 11 × 29. 319 is the sum of three consecutive primes (103 + 107 + 109), Smith number,<ref name=A006753>{{Cite OEIS|A006753|Smith numbers}}</ref> cannot be represented as the sum of fewer than 19 fourth powers, happy number in base 10<ref>{{Cite OEIS|A007770|Happy numbers: numbers whose trajectory under iteration of sum of squares of digits map (see A003132) includes 1}}</ref>

=== 320s ===

==== 320 ====

320 = 26 × 5 = (25) × (2 × 5). 320 is a Leyland number,<ref name=A076980>{{Cite OEIS|A076980|Leyland numbers}}</ref> and maximum determinant of a 10 by 10 matrix of zeros and ones.

==== 321 ====

321 = 3 × 107, a Delannoy number<ref>{{Cite OEIS|A001850|Central Delannoy numbers}}</ref>

==== 322 ====

322 = 2 × 7 × 23. 322 is a sphenic,<ref name=A007304>{{Cite OEIS|A007304|Sphenic numbers}}</ref> nontotient, untouchable,<ref name=A005114>{{Cite OEIS|A005114|Untouchable numbers, also called nonaliquot numbers: impossible values for the sum of aliquot parts function}}</ref> and a Lucas number.<ref>{{Cite OEIS|A000032|Lucas numbers}}</ref> It is also the first unprimeable number to end in 2.

==== 323 ====

==== 324 ====

324 = 22 × 34 = 182. 324 is the sum of four consecutive primes (73 + 79 + 83 + 89), totient sum of the first 32 integers, a square number,<ref>{{Cite OEIS|A000290|2=The squares: a(n) = n^2}}</ref> and an untouchable number.<ref name=A005114 />

==== 325 ====

==== 326 ====

326 = 2 × 163. 326 is a nontotient, noncototient,<ref name=A005278>{{Cite OEIS|A005278|Noncototients}}</ref> and an untouchable number.<ref name=A005114 /> 326 is the sum of the 14 consecutive primes (3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47), lazy caterer number<ref name=A000124>{{Cite OEIS|A000124|Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts}}</ref>

==== 327 ====

327 = 3 × 109. 327 is a perfect totient number,<ref>{{Cite OEIS|A082897|Perfect totient numbers}}</ref> number of compositions of 10 whose run-lengths are either weakly increasing or weakly decreasing<ref>{{cite OEIS|A332835|Number of compositions of n whose run-lengths are either weakly increasing or weakly decreasing}}</ref>

==== 328 ====

328 = 23 × 41. 328 is a refactorable number,<ref name=A033950>{{Cite OEIS|A033950|Refactorable numbers}}</ref> and it is the sum of the first fifteen primes (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47).

==== 329 ====

329 = 7 × 47. 329 is the sum of three consecutive primes (107 + 109 + 113), and a highly cototient number.<ref name=A100827>{{Cite OEIS|A100827|Highly cototient numbers}}</ref>

=== 330s ===

==== 330 ====

330 = 2 × 3 × 5 × 11. 330 is sum of six consecutive primes (43 + 47 + 53 + 59 + 61 + 67), pentatope number (and hence a binomial coefficient <math>\tbinom {11}4 </math>), a pentagonal number,<ref name=A000326>{{Cite OEIS|A000326|Pentagonal numbers}}</ref> divisible by the number of primes below it, and a sparsely totient number.<ref>{{Cite OEIS|A036913|Sparsely totient numbers}}</ref>

==== 331 ====

331 is a prime number, super-prime, cuban prime,<ref name=A002407>{{cite OEIS|A002407|Cuban primes: primes which are the difference of two consecutive cubes}}</ref> a lucky prime,<ref name=A031157>{{cite OEIS|A031157|Numbers that are both lucky and prime}}</ref> sum of five consecutive primes (59 + 61 + 67 + 71 + 73), centered pentagonal number,<ref name=A005891>{{Cite OEIS|A005891|Centered pentagonal numbers}}</ref> centered hexagonal number,<ref name=A003215>{{Cite OEIS|A003215|Hex numbers}}</ref> and Mertens function returns 0.<ref name=A028442>{{Cite OEIS|A028442|2=Numbers n such that Mertens' function is zero}}</ref>

==== 332 ====

332 = 22 × 83, Mertens function returns 0.<ref name=A028442/>

==== 333 ====

333 = 32 × 37, Mertens function returns 0;<ref name=A028442/> repdigit; 2333 is the smallest power of two greater than a googol.

==== 334 ====

334 = 2 × 167, nontotient.<ref>{{Cite OEIS|A003052|Self numbers}}</ref>

==== 335 ====

335 = 5 × 67. 335 is divisible by the number of primes below it, number of Lyndon words of length 12.

==== 336 ====

336 = 24 × 3 × 7, untouchable number,<ref name=A005114/> number of partitions of 41 into prime parts,<ref>{{Cite OEIS|A000607|Number of partitions of n into prime parts}}</ref> largely composite number.<ref name="OEIS-A067128">{{Cite OEIS|A067128|Ramanujan's largely composite numbers}}</ref>

==== 337 ====

337, prime number, emirp, permutable prime with 373 and 733, Chen prime,<ref name=A109611>{{Cite OEIS|A109611|Chen primes}}</ref> star number

==== 338 ====

338 = 2 × 132, nontotient, number of square (0,1)-matrices without zero rows and with exactly 4 entries equal to 1.<ref>{{cite OEIS|A122400|Number of square (0,1)-matrices without zero rows and with exactly n entries equal to 1}}</ref>

==== 339 ====

339 = 3 × 113, Ulam number<ref>{{cite OEIS|A002858|Ulam numbers}}</ref>

=== 340s ===

==== 340 ====

340 = 22 × 5 × 17, sum of eight consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), sum of ten consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), sum of the first four powers of 4 (41 + 42 + 43 + 44), divisible by the number of primes below it, nontotient, noncototient.<ref name=A005278/> Number of [https://oeis.org/A331452/a331452_1.png regions] formed by drawing the line segments connecting any two of the 12 perimeter points of a 3 times 3 grid of squares {{OEIS|id=A331452}} and {{OEIS|id=A255011}}.

==== 341 ====

==== 342 ====

342 = 2 × 32 × 19, pronic number,<ref name=A002378>{{cite OEIS|A002378|2=Oblong (or promic, pronic, or heteromecic) numbers: a(n) = n*(n+1)}}</ref> Untouchable number.<ref name=A005114/>

==== 343 ====

343 = 73, the first nice Friedman number that is composite since 343 = (3 + 4)3. It is the only known example of x2+x+1 = y3, in this case, x=18, y=7. It is z3 in a triplet (x,y,z) such that x5 + y2 = z3.

==== 344 ====

344 = 23 × 43, octahedral number,<ref>{{Cite OEIS|A005900|Octahedral numbers}}</ref> noncototient,<ref name=A005278/> totient sum of the first 33 integers, refactorable number.<ref name=A033950/>

==== 345 ====

345 = 3 × 5 × 23, sphenic number,<ref name=A007304/> idoneal number

==== 346 ====

346 = 2 × 173, Smith number,<ref name=A006753/> noncototient.<ref name=A005278/>

==== 347 ====

347 is a prime number, emirp, safe prime,<ref name=A005385>{{Cite OEIS|A005385|Safe primes}}</ref> Eisenstein prime with no imaginary part, Chen prime,<ref name=A109611/> Friedman prime since 347 = 73 + 4, twin prime with 349, and a strictly non-palindromic number.

==== 348 ====

348 = 22 × 3 × 29, sum of four consecutive primes (79 + 83 + 89 + 97), refactorable number.<ref name=A033950/>

==== 349 ====

349, prime number, twin prime, lucky prime, sum of three consecutive primes (109 + 113 + 127), 5349 - 4349 is a prime number.<ref>{{cite OEIS|A059802|Numbers k such that 5^k - 4^k is prime}}</ref>

=== 350s ===

==== 350 ====

350 = 2 × 52 × 7 = <math>\left\{ {7 \atop 4} \right\}</math>, primitive semiperfect number,<ref>{{Cite OEIS|A006036|Primitive pseudoperfect numbers}}</ref> divisible by the number of primes below it, nontotient, a truncated icosahedron of frequency 6 has 350 hexagonal faces and 12 pentagonal faces.

==== 351 ====

351 = 33 × 13, 26th triangular number,<ref>{{Cite web |title=A000217 - OEIS |url=https://oeis.org/A000217 |access-date=2024-11-28 |website=oeis.org}}</ref> sum of five consecutive primes (61 + 67 + 71 + 73 + 79), member of Padovan sequence<ref>{{Cite OEIS|A000931|Padovan sequence}}</ref> and number of compositions of 15 into distinct parts.<ref>{{cite OEIS|A032020|Number of compositions (ordered partitions) of n into distinct parts}}</ref> * The international calling code for Portugal

==== 352 ====

352 = 25 × 11, the number of n-Queens Problem solutions for n = 9. It is the sum of two consecutive primes (173 + 179), lazy caterer number<ref name=A000124/> * The international calling code for Luxembourg

==== 353 ====

{{Main|353 (number)}} * The international calling code for Republic of Ireland

==== 354 ====

354 = 2 × 3 × 59 = 14 + 24 + 34 + 44,<ref>{{cite OEIS|A000538|Sum of fourth powers: 0^4 + 1^4 + ... + n^4}}</ref><ref>{{cite OEIS| A031971|2=a(n) = Sum_{k=1..n} k^n}}</ref> sphenic number,<ref name=A007304/> nontotient, also SMTP code meaning start of mail input. It is also sum of absolute value of the coefficients of Conway's polynomial. * The international calling code for Iceland

==== 355 ====

355 = 5 × 71, Smith number,<ref name=A006753/> Mertens function returns 0,<ref name=A028442/> divisible by the number of primes below it.<ref>{{Cite web |title=A057809 - OEIS |url=https://oeis.org/A057809 |access-date=2024-11-19 |website=oeis.org}}</ref> The cototient of 355 is 75,<ref>{{Cite web |title=A051953 - OEIS |url=https://oeis.org/A051953 |access-date=2024-11-19 |website=oeis.org}}</ref> where 75 is the product of its digits (3 x 5 x 5 = 75).

The numerator of the best simplified rational approximation of pi having a denominator of four digits or fewer. This fraction (355/113) is known as Milü and provides an extremely accurate approximation for pi, being accurate to seven digits.

==== 356 ====

356 = 22 × 89, Mertens function returns 0.<ref name=A028442/>

==== 357 ====

357 = 3 × 7 × 17, sphenic number.<ref name=A007304/>

==== 358 ====

358 = 2 × 179, sum of six consecutive primes (47 + 53 + 59 + 61 + 67 + 71), Mertens function returns 0,<ref name=A028442/> number of ways to partition {1,2,3,4,5} and then partition each cell (block) into subcells.<ref>{{cite OEIS|A000258|Expansion of e.g.f. exp(exp(exp(x)-1)-1)}}</ref> * The international calling code for Finland

==== 359 ====

=== 360s ===

==== 360 ====

==== 361 ====

361 = 192. 361 is a centered triangular number,<ref name=A005448>{{Cite OEIS|A005448|Centered triangular numbers}}</ref> centered octagonal number, centered decagonal number,<ref>{{Cite OEIS|A062786|Centered 10-gonal numbers}}</ref> member of the Mian–Chowla sequence;<ref>{{Cite OEIS|A005282|Mian-Chowla sequence}}</ref> also the number of positions on a standard 19 x 19 Go board.

==== 362 ====

362 = 2 × 181 = σ2(19): sum of squares of divisors of 19,<ref>{{cite OEIS|A001157|2=a(n) = sigma_2(n): sum of squares of divisors of n}}</ref> Mertens function returns 0,<ref name=A028442/> nontotient, noncototient.<ref name=A005278/>

==== 363 ====

==== 364 ====

364 = 22 × 7 × 13, tetrahedral number,<ref name =A000292>{{Cite OEIS|A000292|2=Tetrahedral numbers (or triangular pyramidal)}}</ref> sum of twelve consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), Mertens function returns 0,<ref name=A028442/> nontotient. It is a repdigit in base 3 (111111), base 9 (444), base 25 (EE), base 27 (DD), base 51 (77) and base 90 (44), the sum of six consecutive powers of 3 (1 + 3 + 9 + 27 + 81 + 243), and because it is the twelfth non-zero tetrahedral number.<ref name =A000292/>

==== 365 ====

==== 366 ====

366 = 2 × 3 × 61, sphenic number,<ref name=A007304/> Mertens function returns 0,<ref name=A028442/> noncototient,<ref name=A005278/> number of complete partitions of 20,<ref>{{cite OEIS|A126796|Number of complete partitions of n}}</ref> 26-gonal and 123-gonal. Also the number of days in a leap year.

==== 367 ====

367 is a prime number, a lucky prime,<ref name=A031157/> Perrin number,<ref>{{Cite OEIS|A001608|Perrin sequence}}</ref> happy number, prime index prime and a strictly non-palindromic number.

==== 368 ====

368 = 24 × 23. It is also a Leyland number.<ref name=A076980/>

==== 369 ====

=== 370s ===

==== 370 ====

370 = 2 × 5 × 37, sphenic number,<ref name=A007304/> sum of four consecutive primes (83 + 89 + 97 + 101), nontotient, with 369 part of a Ruth–Aaron pair with only distinct prime factors counted, Base 10 Armstrong number since 33 + 73 + 03 = 370.

==== 371 ====

371 = 7 × 53, sum of three consecutive primes (113 + 127 + 131), sum of seven consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67), sum of the primes from its least to its greatest prime factor,<ref>{{Cite OEIS|A055233|Composite numbers equal to the sum of the primes from their smallest prime factor to their largest prime factor}}</ref> the next such composite number is 2935561623745, Armstrong number since 33 + 73 + 13 = 371.

==== 372 ====

372 = 22 × 3 × 31, sum of eight consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61), noncototient,<ref name=A005278/> untouchable number,<ref name=A005114/> --> refactorable number.<ref name=A033950/>

==== 373 ====

373, prime number, balanced prime,<ref>{{Cite OEIS|A006562|Balanced primes}}</ref> one of the rare primes to be both right and left-truncatable (two-sided prime),<ref name=A020994>{{Cite OEIS|A020994|Primes that are both left-truncatable and right-truncatable}}</ref> sum of five consecutive primes (67 + 71 + 73 + 79 + 83), sexy prime with 367 and 379, permutable prime with 337 and 733, palindromic prime in 3 consecutive bases: 5658 = 4549 = 37310 and also in base 4: 113114.

==== 374 ====

374 = 2 × 11 × 17, sphenic number,<ref name=A007304/> nontotient, 3744 + 1 is prime.<ref>{{cite OEIS|A000068|Numbers k such that k^4 + 1 is prime}}</ref>

==== 375 ====

375 = 3 × 53, number of regions in regular 11-gon with all diagonals drawn.<ref>{{cite OEIS|A007678|Number of regions in regular n-gon with all diagonals drawn}}</ref>

==== 376 ====

376 = 23 × 47, pentagonal number,<ref name=A000326/> 1-automorphic number,<ref>{{Cite OEIS|A003226|Automorphic numbers}}</ref> nontotient, refactorable number.<ref name=A033950/>

==== 377 ==== {{Main article|377 (number)}}

==== 378 ====

378 = 2 × 33 × 7, 27th triangular number,<ref>{{Cite web |title=A000217 - OEIS |url=https://oeis.org/A000217 |access-date=2024-11-28 |website=oeis.org}}</ref> cake number,<ref>{{Cite web |title=A000217 - OEIS |url=https://oeis.org/A000217 |access-date=2024-11-28 |website=oeis.org}}</ref> hexagonal number,<ref name=A000384>{{Cite OEIS|A000384|Hexagonal numbers}}</ref> Smith number.<ref name=A006753/>

==== 379 ====

379 is a prime number, Chen prime,<ref name=A109611/> lazy caterer number<ref name=A000124/> and a happy number in base 10. It is the sum of the first 15 odd primes (3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53). 379! - 1 is prime.

=== 380s ===

==== 380 ====

380 = 22 × 5 × 19, pronic number,<ref name=A002378/> number of regions into which a figure made up of a row of 6 adjacent congruent rectangles is divided upon drawing diagonals of all possible rectangles.<ref>{{Cite OEIS|A306302|Number of regions into which a figure made up of a row of n adjacent congruent rectangles is divided upon drawing diagonals of all possible rectangles}}</ref>

==== 381 ====

381 = 3 × 127, palindromic in base 2 and base 8.

381 is the sum of the first 16 prime numbers (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53).

==== 382 ====

382 = 2 × 191, sum of ten consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), Smith number.<ref name=A006753/>

==== 383 ====

383, prime number, safe prime,<ref name="A005385">{{Cite OEIS|A005385|Safe primes}}</ref> Woodall prime,<ref>{{Cite OEIS|A050918|Woodall primes}}</ref> Thabit number, Eisenstein prime with no imaginary part, palindromic prime. It is also the first number where the sum of a prime and the reversal of the prime is also a prime.<ref>{{Cite OEIS|A072385|Primes which can be represented as the sum of a prime and its reverse}}</ref> 4383 - 3383 is prime.

==== 384 ====

==== 385 ====

385 = 5 × 7 × 11, sphenic number,<ref name=A007304/> square pyramidal number,<ref>{{Cite OEIS|A000330|Square pyramidal numbers}}</ref> the number of integer partitions of 18.

385 = 102 + 92 + 82 + 72 + 62 + 52 + 42 + 32 + 22 + 12

==== 386 ====

386 = 2 × 193, nontotient, noncototient,<ref name=A005278/> centered heptagonal number,<ref name=A069099>{{Cite OEIS|A069099|Centered heptagonal numbers}}</ref> number of surface points on a cube with edge-length 9.<ref>{{cite OEIS|A005897|2=a(n) = 6*n^2 + 2 for n > 0, a(0)=1}}</ref>

==== 387 ====

387 = 32 × 43, number of graphical partitions of 22.<ref>{{cite OEIS|A000569|Number of graphical partitions of 2n}}</ref>

==== 388 ====

388 = 22 × 97 = solution to postage stamp problem with 6 stamps and 6 denominations,<ref>{{cite OEIS|A084192|2=Array read by antidiagonals: T(n,k) = solution to postage stamp problem with n stamps and k denominations (n >= 1, k >= 1)}}</ref> number of uniform rooted trees with 10 nodes.<ref>{{cite OEIS|A317712|Number of uniform rooted trees with n nodes}}</ref>

==== 389 ====

389, prime number, emirp, Eisenstein prime with no imaginary part, Chen prime,<ref name=A109611/> highly cototient number,<ref name=A100827/> strictly non-palindromic number. Smallest conductor of a rank 2 Elliptic curve.

=== 390s ===

==== 390 ====

390 = 2 × 3 × 5 × 13, sum of four consecutive primes (89 + 97 + 101 + 103), nontotient, :<math>\sum_{n=0}^{10}{390}^{n}</math> is prime<ref name=A162862>{{cite OEIS|A162862|Numbers n such that n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime}}</ref>

==== 391 ====

391 = 17 × 23, Smith number,<ref name=A006753/> centered pentagonal number.<ref name=A005891/>

==== 392 ====

392 = 23 × 72, Achilles number.

==== 393 ====

393 = 3 × 131, Blum integer, Mertens function returns 0.<ref name=A028442/>

==== 394 ====

394 = 2 × 197 = S5 a Schröder number,<ref>{{Cite OEIS|A006318|2=Large Schröder numbers}}</ref> nontotient, noncototient.<ref name=A005278/>

==== 395 ====

395 = 5 × 79, sum of three consecutive primes (127 + 131 + 137), sum of five consecutive primes (71 + 73 + 79 + 83 + 89), number of (unordered, unlabeled) rooted trimmed trees with 11 nodes.<ref>{{cite OEIS|A002955|Number of (unordered, unlabeled) rooted trimmed trees with n nodes}}</ref>

==== 396 ====

396 = 22 × 32 × 11, sum of twin primes (197 + 199), totient sum of the first 36 integers, refactorable number,<ref name=A033950/> Harshad number, digit-reassembly number.

==== 397 ====

397, prime number, cuban prime,<ref name=A002407/> centered hexagonal number.<ref name=A003215/>

==== 398 ====

398 = 2 × 199, nontotient. :<math>\sum_{n=0}^{10}{398}^{n}</math> is prime<ref name=A162862/>

==== 399 ====

399 = 3 × 7 × 19, sphenic number,<ref name=A007304/> smallest Lucas–Carmichael number, and a Leyland number of the second kind<ref>{{Cite OEIS|A045575|Leyland numbers of the second kind}}</ref> {{no wrap|(<math>4^5-5^4</math>).}} 399! + 1 is prime.

399 is the largest number whose base 10 digit sum is larger than the square root of the number: 3 + 9 + 9 = 21, which is larger than 19.975.

== References ==

Category:Integers