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Natural number
300 (three hundred) is the natural number following 299 and preceding 301.
300 is a composite number and the 24th triangular number.[1] It is also a second hexagonal number.[2]
Integers from 301 to 399[edit]319 = 11 × 29. 319 is the sum of three consecutive primes (103 + 107 + 109), Smith number,[3] cannot be represented as the sum of fewer than 19 fourth powers, happy number in base 10[4]
320 = 26 × 5 = (25) × (2 × 5). 320 is a Leyland number,[5] and maximum determinant of a 10 by 10 matrix of zeros and ones.
321 = 3 × 107, a Delannoy number[6]
322 = 2 × 7 × 23. 322 is a sphenic,[7] nontotient, untouchable,[8] and a Lucas number.[9] It is also the first unprimeable number to end in 2.
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,[10] and an untouchable number.[8]
326 = 2 × 163. 326 is a nontotient, noncototient,[11] and an untouchable number.[8] 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[12]
327 = 3 × 109. 327 is a perfect totient number,[13] number of compositions of 10 whose run-lengths are either weakly increasing or weakly decreasing[14]
328 = 23 × 41. 328 is a refactorable number,[15] 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.[16]
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 ( 11 4 ) {\displaystyle {\tbinom {11}{4}}} ), a pentagonal number,[17] divisible by the number of primes below it, and a sparsely totient number.[18]
331 is a prime number, super-prime, cuban prime,[19] a lucky prime,[20] sum of five consecutive primes (59 + 61 + 67 + 71 + 73), centered pentagonal number,[21] centered hexagonal number,[22] and Mertens function returns 0.[23]
332 = 22 × 83, Mertens function returns 0.[23]
333 = 32 × 37, Mertens function returns 0;[23] repdigit; 2333 is the smallest power of two greater than a googol.
334 = 2 × 167, nontotient.[24]
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,[8] number of partitions of 41 into prime parts,[25] largely composite number.[26]
337, prime number, emirp, permutable prime with 373 and 733, Chen prime,[27] star number
338 = 2 × 132, nontotient, number of square (0,1)-matrices without zero rows and with exactly 4 entries equal to 1.[28]
339 = 3 × 113, Ulam number[29]
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.[11] Number of regions formed by drawing the line segments connecting any two of the 12 perimeter points of a 3 times 3 grid of squares (sequence A331452 in the OEIS) and (sequence A255011 in the OEIS).
342 = 2 × 32 × 19, pronic number,[30] Untouchable number.[8]
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,[31] noncototient,[11] totient sum of the first 33 integers, refactorable number.[15]
345 = 3 × 5 × 23, sphenic number,[7] idoneal number
346 = 2 × 173, Smith number,[3] noncototient.[11]
347 is a prime number, emirp, safe prime,[32] Eisenstein prime with no imaginary part, Chen prime,[27] 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.[15]
349, prime number, twin prime, lucky prime, sum of three consecutive primes (109 + 113 + 127), 5349 - 4349 is a prime number.[33]
350 = 2 × 52 × 7 = { 7 4 } {\displaystyle \left\{{7 \atop 4}\right\}} , primitive semiperfect number,[34] 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,[35] sum of five consecutive primes (61 + 67 + 71 + 73 + 79), member of Padovan sequence[36] and number of compositions of 15 into distinct parts.[37]
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[12]
354 = 2 × 3 × 59 = 14 + 24 + 34 + 44,[38][39] sphenic number,[7] 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,[3] Mertens function returns 0,[23] divisible by the number of primes below it.[40] The cototient of 355 is 75,[41] 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.[23]
357 = 3 × 7 × 17, sphenic number.[7]
358 = 2 × 179, sum of six consecutive primes (47 + 53 + 59 + 61 + 67 + 71), Mertens function returns 0,[23] number of ways to partition {1,2,3,4,5} and then partition each cell (block) into subcells.[42]
361 = 192. 361 is a centered triangular number,[43] centered octagonal number, centered decagonal number,[44] member of the Mian–Chowla sequence;[45] 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,[46] Mertens function returns 0,[23] nontotient, noncototient.[11]
364 = 22 × 7 × 13, tetrahedral number,[47] sum of twelve consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), Mertens function returns 0,[23] 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.[47]
366 = 2 × 3 × 61, sphenic number,[7] Mertens function returns 0,[23] noncototient,[11] number of complete partitions of 20,[48] 26-gonal and 123-gonal. Also the number of days in a leap year.
367 is a prime number, a lucky prime,[20] Perrin number,[49] happy number, prime index prime and a strictly non-palindromic number.
368 = 24 × 23. It is also a Leyland number.[5]
370 = 2 × 5 × 37, sphenic number,[7] 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,[50] 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,[11] untouchable number,[8] --> refactorable number.[15]
373, prime number, balanced prime,[51] one of the rare primes to be both right and left-truncatable (two-sided prime),[52] 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,[7] nontotient, 3744 + 1 is prime.[53]
375 = 3 × 53, number of regions in regular 11-gon with all diagonals drawn.[54]
376 = 23 × 47, pentagonal number,[17] 1-automorphic number,[55] nontotient, refactorable number.[15]
377 = 13 × 29, Fibonacci number, a centered octahedral number,[56] a Lucas and Fibonacci pseudoprime, the sum of the squares of the first six primes.
378 = 2 × 33 × 7, 27th triangular number,[57] cake number,[58] hexagonal number,[59] Smith number.[3]
379 is a prime number, Chen prime,[27] lazy caterer number[12] 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,[30] 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.[60]
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.[3]
383, prime number, safe prime,[32] Woodall prime,[61] 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.[62] 4383 - 3383 is prime.
385 = 5 × 7 × 11, sphenic number,[7] square pyramidal number,[63] the number of integer partitions of 18.
385 = 102 + 92 + 82 + 72 + 62 + 52 + 42 + 32 + 22 + 12
386 = 2 × 193, nontotient, noncototient,[11] centered heptagonal number,[64] number of surface points on a cube with edge-length 9.[65]
387 = 32 × 43, number of graphical partitions of 22.[66]
388 = 22 × 97 = solution to postage stamp problem with 6 stamps and 6 denominations,[67] number of uniform rooted trees with 10 nodes.[68]
389, prime number, emirp, Eisenstein prime with no imaginary part, Chen prime,[27] highly cototient number,[16] 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,
391 = 17 × 23, Smith number,[3] centered pentagonal number.[21]
392 = 23 × 72, Achilles number.
393 = 3 × 131, Blum integer, Mertens function returns 0.[23]
394 = 2 × 197 = S5 a Schröder number,[70] nontotient, noncototient.[11]
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.[71]
396 = 22 × 32 × 11, sum of twin primes (197 + 199), totient sum of the first 36 integers, refactorable number,[15] Harshad number, digit-reassembly number.
397, prime number, cuban prime,[19] centered hexagonal number.[22]
398 = 2 × 199, nontotient.
399 = 3 × 7 × 19, sphenic number,[7] smallest Lucas–Carmichael number, and a Leyland number of the second kind[72] ( 4 5 − 5 4 {\displaystyle 4^{5}-5^{4}} ). 399! + 1 is prime.
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