300 (number)#315

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

{{Main|301 (number)}}

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{{Main|303 (number)}}

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{{Main|314 (number)}}

315 = 3² × 5 × 7 = $D\_\{7,3\}\; \backslash !$, rencontres number, highly composite odd number, having 12 divisors.{{cite OEIS|A053624|Highly composite odd numbers (1): where d(n) increases to a record}}

It is a Harshad number, as it is divisible by the sum of its digits.{{Cite OEIS|A005349|Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits.}}

It is a Zuckerman number, as it is divisible by the product of its digits.{{Cite OEIS|A007602|Numbers that are divisible by the product of their digits.}}

316 = 2² × 79, a centered triangular number{{Cite OEIS|A005448|Centered triangular numbers}} and a centered heptagonal number.{{Cite OEIS|A069099|Centered heptagonal numbers}}

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

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

{{Main|318 (number)}}

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

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

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

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

{{Main|323 (number)}}

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,{{Cite OEIS|A000290|2=The squares: a(n) = n^2}} and an untouchable number.

{{Main|325 (number)}}

326 = 2 × 163. 326 is a nontotient, noncototient,{{Cite OEIS|A005278|Noncototients}} and an untouchable number. 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{{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}}

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

328 = 2³ × 41. 328 is a refactorable number,{{Cite OEIS|A033950|Refactorable numbers}} 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 = 7 × 47. 329 is the sum of three consecutive primes (107 + 109 + 113), and a highly cototient number.{{Cite OEIS|A100827|Highly cototient numbers}}

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 $\backslash tbinom\; \{11\}4$), a pentagonal number,{{Cite OEIS|A000326|Pentagonal numbers}} divisible by the number of primes below it, and a sparsely totient number.{{Cite OEIS|A036913|Sparsely totient numbers}}

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

332 = 2² × 83, Mertens function returns 0.

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

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

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

336 = 2⁴ × 3 × 7, untouchable number, number of partitions of 41 into prime parts,{{Cite OEIS|A000607|Number of partitions of n into prime parts}} largely composite number.{{Cite OEIS|A067128|Ramanujan's largely composite numbers}}

337, prime number, emirp, permutable prime with 373 and 733, Chen prime, star number

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

339 = 3 × 113, Ulam number{{cite OEIS|A002858|Ulam numbers}}

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. 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}}.

{{Main article|341 (number)}}

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

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 = 2³ × 43, octahedral number,{{Cite OEIS|A005900|Octahedral numbers}} noncototient, totient sum of the first 33 integers, refactorable number.

345 = 3 × 5 × 23, sphenic number, idoneal number

346 = 2 × 173, Smith number, noncototient.

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

348 = 2² × 3 × 29, sum of four consecutive primes (79 + 83 + 89 + 97), refactorable number.

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

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

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

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

{{Main|353 (number)}}

354 = 2 × 3 × 59 = 1⁴ + 2⁴ + 3⁴ + 4⁴,{{cite OEIS|A000538|Sum of fourth powers: 0^4 + 1^4 + ... + n^4}}{{cite OEIS|

A031971|2=a(n) = Sum_{k=1..n} k^n}} sphenic number, nontotient, also SMTP code meaning start of mail input. It is also sum of absolute value of the coefficients of Conway's polynomial.

355 = 5 × 71, Smith number, Mertens function returns 0, divisible by the number of primes below it.{{Cite web |title=A057809 - OEIS |url=https://oeis.org/A057809 |access-date=2024-11-19 |website=oeis.org}} The cototient of 355 is 75,{{Cite web |title=A051953 - OEIS |url=https://oeis.org/A051953 |access-date=2024-11-19 |website=oeis.org}} 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 = 2² × 89, Mertens function returns 0.

357 = 3 × 7 × 17, sphenic number.

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

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{{Main|360 (number)}}

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

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

{{Main|363 (number)}}

364 = 2² × 7 × 13, tetrahedral number,{{Cite OEIS|A000292|2=Tetrahedral numbers (or triangular pyramidal)}} sum of twelve consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), Mertens function returns 0, 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.

{{Main|365 (number)}}

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

367 is a prime number, a lucky prime, Perrin number,{{Cite OEIS|A001608|Perrin sequence}} happy number, prime index prime and a strictly non-palindromic number.

368 = 2⁴ × 23. It is also a Leyland number.

{{Main|369 (number)}}

370 = 2 × 5 × 37, sphenic number, 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 = 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,{{Cite OEIS|A055233|Composite numbers equal to the sum of the primes from their smallest prime factor to their largest prime factor}} the next such composite number is 2935561623745, Armstrong number since 3³ + 7³ + 1³ = 371.

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

373, prime number, balanced prime,{{Cite OEIS|A006562|Balanced primes}} one of the rare primes to be both right and left-truncatable (two-sided prime), 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 = 2 × 11 × 17, sphenic number, nontotient, 374⁴ + 1 is prime.{{cite OEIS|A000068|Numbers k such that k^4 + 1 is prime}}

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

376 = 2³ × 47, pentagonal number, 1-automorphic number,{{Cite OEIS|A003226|Automorphic numbers}} nontotient, refactorable number.

377 = 13 × 29, Fibonacci number, a centered octahedral number,{{cite OEIS|A001845|Centered octahedral numbers (crystal ball sequence for cubic lattice)}} a Lucas and Fibonacci pseudoprime, the sum of the squares of the first six primes.

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

379 is a prime number, Chen prime, lazy caterer number 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.

380 = 2² × 5 × 19, pronic number, 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.{{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}}

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 = 2 × 191, sum of ten consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), Smith number.

383, prime number, safe prime, Woodall prime,{{Cite OEIS|A050918|Woodall primes}} 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.{{Cite OEIS|A072385|Primes which can be represented as the sum of a prime and its reverse}} 4³⁸³ - 3³⁸³ is prime.

{{Main|384 (number)}}

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

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

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

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

388 = 2² × 97 = solution to postage stamp problem with 6 stamps and 6 denominations,{{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)}} number of uniform rooted trees with 10 nodes.{{cite OEIS|A317712|Number of uniform rooted trees with n nodes}}

389, prime number, emirp, Eisenstein prime with no imaginary part, Chen prime, highly cototient number, strictly non-palindromic number. Smallest conductor of a rank 2 Elliptic curve.

390 = 2 × 3 × 5 × 13, sum of four consecutive primes (89 + 97 + 101 + 103), nontotient,

:$\backslash sum\_\{n=0\}^\{10\}\{390\}^\{n\}$ is prime{{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}}

391 = 17 × 23, Smith number, centered pentagonal number.

392 = 2³ × 7², Achilles number.

393 = 3 × 131, Blum integer, Mertens function returns 0.

394 = 2 × 197 = S₅ a Schröder number,{{Cite OEIS|A006318|2=Large Schröder numbers}} nontotient, noncototient.

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.{{cite OEIS|A002955|Number of (unordered, unlabeled) rooted trimmed trees with n nodes}}

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

397, prime number, cuban prime, centered hexagonal number.

398 = 2 × 199, nontotient.

:$\backslash sum\_\{n=0\}^\{10\}\{398\}^\{n\}$ is prime

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

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{{Integers|3}}

Category:Integers