322

In mathematics

300 is a composite number and the 24th triangular number. It is also a second hexagonal number.

Integers from 301 to 399

300s

301 is the first 6-hyperperfect number.

An adult nematode worm has exactly 302 cells in its nervous system.

303 is a semiprime number. There are 303 compositions of 10 where they cannot be viewed as a stack. There are 303 bipartite graphs with 8 vertices.

304 = 24 × 19. It is a primitive semiperfect number because it is a semiperfect number that is not divisible by any other semiperfect number. It is an untouchable number because it is not equal to the sum of any number's proper divisors. 304 is a nontotient number because it is an even number and phi(x) = 304 has no solution. It is the sum of consecutive primes in two different ways:

304 = 41+43+47+53+59+61 = 23+29+31+37+41+43+47+53.

305 = 5 × 61. It is the fifth hexagonal prism number which is defined by (n+1)(3n2+3n+1). It is the convolution of the first 7 primes with themselves. It is the hypotenuse of two Pythagorean triples: 3052=2072+2242=1362+2732.

306 = 2 × 32 × 17. It is the 17th oblong number meaning that it is equal to 17*18. It is an untouchable number meaning that it cannot be equal to the sum of proper factors in any number. It is the sum of four consecutive primes (71+73+79+83).

There are 306 triangular numbers with 5 digits.

307 is an isolated (i.e., not twin) prime, but because 309 is a semiprime, 307 is a Chen prime. 307 is the third non-palindromic number to have a palindromic square. 3072=94249.

307 is one of only 16 natural numbers for which the imaginary quadratic field

Q

(

−

310s

310 = 2 × 5 × 31. It is a sphenic number meaning that it has 3 prime factors. It is a noncototient number because m − φ(m) = 310 has no solutions. There are 310 Dyks 11 paths with strictly intersecting peaks. The sum of the divisors of 310 is a perfect square.

311 is a twin prime with 313, an irregular prime, an emirp, and a permutable prime with 113 and 131. It is an Eisenstein prime with no imaginary part and real part of the form

3

n

−

1

{\displaystyle 3n-1}

and a Gaussian prime with no imaginary part and real part of the form

4

n

−

1

{\displaystyle 4n-1}

.

It can be expressed as a sum of consecutive primes in four different ways: as a sum of three consecutive primes (101 + 103 + 107), as a sum of five consecutive primes (53 + 59 + 61 + 67 + 71), as a sum of seven consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59), and as a sum of eleven consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47).

311 is a strictly non-palindromic number, as it is not palindromic in any base between base 2 and base 309.

311 is the smallest positive integer d such that the imaginary quadratic field Q(√–d) has a class number of 19.

4311 - 3311 is a prime number.

320s

320 = 26 × 5 = (25) × (2 × 5). It is a Leyland number, and the maximum determinant of a 10 by 10 matrix of zeros and ones.

321 = 3 × 107. It is a Delannoy number

322 = 2 × 7 × 23. It is a sphenic, a nontotient, an untouchable number, and a Lucas number. It is also the first unprimeable number to end in 2.

323 is a semiprime, and the product of two consecutive prime numbers (17 × 19). It is also the sum of nine consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53) and the sum of the 13 consecutive primes (5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47)

323 is the eighth Motzkin number,

M

8

{\displaystyle M_{8}}

, meaning there are 323 ways to draw non-intersecting chords between eight points on a circle.

323 is the first Lucas pseudoprime with parameters (P, Q) defined by Selfridge's method. Additionally, it is the first Fibonacci pseudoprime (Lucas pseudoprime with P = 1 and Q = -1).

324 = 22 × 34. It is a regular number, an abundant number, a Nialpdrome, an ulam number, a powerful number, and an untouchable number, also called a nonaliquot number. It is the totient sum of the first 32 integers. It is the largest possible product of a set of positive integers with a sum of 16.

It is a perfect square number, since 324 equals 18^2, which is 18 x 18. It is also a Harshad number, sometimes called a Niven number, since the digit sum of 324 equals to 9 and 324 is a multiple of 9.

325 = 52 × 13. It is the smallest number to be the sum of two squares in 3 different ways: 12 + 182, 62 + 172 and 102 + 152. It is the smallest (and only known) 3-hyperperfect number.

330s

330 = 2 × 3 × 5 × 11. It is a pentatope number (a binomial coefficient

(

11

4

)

{\displaystyle {\tbinom {11}{4}}}

), a pentagonal number, and a sparsely totient number. It is sum of six consecutive primes (43 + 47 + 53 + 59 + 61 + 67).

331 is a prime number, a super-prime, a cuban prime, a lucky prime, a centered pentagonal number, a centered hexagonal number, and a zero of Mertens function. It is the sum of five consecutive primes (59 + 61 + 67 + 71 + 73).

332 = 22 × 83. It is a zero of Mertens function.

333 = 32 × 37. It is a harshad number, an odious number, and a zero of Mertens function.

It is also a palindromic number that is a repdigit in bases 8, 10, and 36. It is also the smallest multidigit composite palindrome such that the sum of its proper divisors is also a palindrome.

2333 is the smallest power of two greater than a googol.

There is a total of 333 septahexes.

334 = 2 × 167. It is a nontotient.

335 = 5 × 67. There are 335 Lyndon words of length 12.

336 = 24 × 3 × 7. It is an untouchable number and a largely composite number. There are 336 partitions of 41 into prime parts.

337 is a prime number, an emirp, a permutable prime, and a Chen prime.

340s

340 = 22 × 5 × 17. It is a noncototient and a nontotient.

It is the sum of the first four powers of 4 (41 + 42 + 43 + 44), the sum of eight consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), and the sum of ten consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53).

There are 340 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).

341 is an octagonal number, a centered cube number, and a super-Poulet number. It is a palindrome and repdigit in bases 2 (1010101012), 4 (111114), 8 (5258), 17 (13117) and 30 (BB30). It is the sum of seven consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61).

341 is the smallest Fermat pseudoprime; it is the least composite odd modulus m greater than the base b, that satisfies the Fermat property "bm−1 − 1 is divisible by m", for bases up to 128 of b = 2, 15, 60, 63, 78, and 108.

342 = 2 × 32 × 19. It is a pronic number, and an 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. It is an octahedral number, a noncototient, a refactorable number, and the totient sum of the first 33 integers.

345 = 3 × 5 × 23. It is a sphenic number and an idoneal number.

346 = 2 × 173. It is a Smith number and a noncototient.

347 is a prime number, an emirp, a safe prime, an Eisenstein prime with no imaginary part, a Chen prime, a twin prime with 349, a strictly non-palindromic number, and a Friedman prime since 347 = 73 + 4.

350s

350 = 2 × 52 × 7. It is a primitive semiperfect number and a nontotient. A truncated icosahedron of frequency 6 has 350 hexagonal faces and 12 pentagonal faces.

350=

{

7

4

}

{\displaystyle \left\{{7 \atop 4}\right\}}

, making 350 a stirling number of the second kind.

351 = 33 × 13. It is a member of the Padovan sequence and the 26th triangular number. It is the sum of five consecutive primes (61 + 67 + 71 + 73 + 79). There are 351 compositions of 15 into distinct parts.

352 = 25 × 11. It is a lazy caterer number and the sum of two consecutive primes (173 + 179). There are 352 n-Queens Problem solutions for n = 9.

354 = 2 × 3 × 59 = 14 + 24 + 34 + 44. It is a sphenic number and a nontotient. It is also sum of absolute value of the coefficients of Conway's polynomial.

355 = 5 × 71. It is a Smith number and a zero of Mertens function. The cototient of 355 is 75, where 75 is the product of its digits (3 x 5 x 5 = 75).

It is the numerator of, 355/113, the best simplified rational approximation of pi having a denominator of four digits or fewer, known as Milü.

356 = 22 × 89. It is a zero of Mertens function.

357 = 3 × 7 × 17. It is a sphenic number.

358 = 2 × 179. It is a zero of Mertens function and the sum of six consecutive primes (47 + 53 + 59 + 61 + 67 + 71). There are 358 ways to partition {1,2,3,4,5} and then partition each cell (block) into subcells.

360s

361 = 192. 361 is a centered triangular number, a centered octagonal number, a centered decagonal number and a member of the Mian–Chowla sequence. There are 361 intersections on a standard 19 x 19 Go board.

362 = 2 × 181. It is a zero of Mertens function, a nontotient, a noncototient.

362= σ2(19), the sum of squares of divisors of 19.

363=3 × 112. It is a deficient number, a perfect totient number, a zero of Mertens function, and a repdigit (BB) in base 32. It is a palindromic number in bases 3, 10, 11 and 32. It is the sum of nine consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59) and the sum of five consecutive powers of 3 (3 + 9 + 27 + 81 + 243).

363 can be expressed as the sum of three squares in four different ways:

363 = 112 + 112 + 112 = 52 + 72 + 172 = 12 + 12 + 192 = 132 + 132 + 52.

363 cubits is the solution given to Rhind Mathematical Papyrus question 50 – find the side length of an octagon with the same area as a circle 9 khet in diameter.

364 = 22 × 7 × 13. It is a tetrahedral number, a zero of Mertens function, a nontotient, and the sum of twelve consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53).

It is a repdigit in base 3 (111111), base 9 (444), base 25 (EE), base 27 (DD), base 51 (77) and base 90 (44).

366 = 2 × 3 × 61. It is a sphenic number, a zero of Mertens function, a noncototient, a 26-gonal number, and a 123-gonal number. There are 366 complete partitions of 20.

There are 366 days in a leap year.

370s

370 = 2 × 5 × 37. It is a sphenic number, a nontotient, and a Base 10 Armstrong number since 33 + 73 + 03 = 370. It forms a Ruth–Aaron pair with only distinct prime factors counted with 369. It is the sum of four consecutive primes (83 + 89 + 97 + 101).

371 = 7 × 53. It is an Armstrong number since 33 + 73 + 13 = 371. It is the sum of the primes from its least to its greatest prime factor, the next such composite number is 2935561623745. It is the sum of three consecutive primes (113 + 127 + 131) and the sum of seven consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67).

372 = 22 × 3 × 31. It is a noncototient, an untouchable number, and a refactorable number. It is the sum of eight consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61).

373 is a prime number, a balanced prime, a right and left-truncatable (two-sided prime), a sexy prime with 367 and 379, and a permutable prime with 337 and 733. It is also a palindromic prime in 3 consecutive bases: 5658 = 4549 = 37310 and also in base 4: 113114. It is the sum of five consecutive primes (67 + 71 + 73 + 79 + 83).

374 = 2 × 11 × 17. It is a sphenic number and a nontotient. 3744 + 1 is prime.

375 = 3 × 53. There are 375 regions in regular 11-gon with all diagonals drawn.

376 = 23 × 47. It is a pentagonal number, a 1-automorphic number, a nontotient, and a refactorable number.

377 is a semiprime and a deficient number. 377 is the 7th centered octahedral number and the 14th nonzero member of the Fibonacci sequence.

378 = 2 × 33 × 7. It is a cake number, a hexagonal number, and a Smith number. It is the 27th triangular number.

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

380s

380 = 22 × 5 × 19. It is a pronic number. There are 380 regions when a figure made up of a row of 6 adjacent congruent rectangles is divided by drawing the diagonals of all possible rectangles.

381 = 3 × 127. It is 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. It is a Smith number. It is the sum of ten consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59).

383 is a prime number, a safe prime, a Woodall prime, a Thabit number, an Eisenstein prime with no imaginary part, and a palindromic prime. It is also the first number where the sum of a prime and the reversal of the prime is also a prime. 4383 - 3383 is prime.

385 = 5 × 7 × 11. It is a sphenic number and a square pyramidal number. There are 385 integer partitions of 18.

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

386 = 2 × 193. It is a nontotient, a noncototient, and a centered heptagonal number. There are 388 surface points on a cube with edge-length 9.

387 = 32 × 43. There are 387 graphical partitions of 22.

388 = 22 × 97. It is the solution to the postage stamp problem with 6 stamps and 6 denominations. There are 388 uniform rooted trees with 10 nodes.

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

390s

390 = 2 × 3 × 5 × 13. It is a nontotient and the sum of four consecutive primes (89 + 97 + 101 + 103).

∑

n

=

0

10

390

n

{\displaystyle \sum _{n=0}^{10}{390}^{n}}

is prime

391 = 17 × 23. It is a Smith number and a centered pentagonal number.

392 = 23 × 72. It is an Achilles number.

393 = 3 × 131. It is a Blum integer and a zero of Mertens function.

394 = 2 × 197 = S5 It is a Schröder number, a nontotient, and a noncototient.

395 = 5 × 79. There are 395 (unordered, unlabeled) rooted trimmed trees with 11 nodes.

395 is sum of three consecutive primes (127 + 131 + 137) and the sum of five consecutive primes (71 + 73 + 79 + 83 + 89).

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

397 is a prime number, a cuban prime, and a centered hexagonal number.

398 = 2 × 199. It is a nontotient.