360 (number)

360 (three hundred [and] sixty) is the

In mathematics

• 360 is a highly composite number^[1] and one of only seven numbers such that no number less than twice as much has more divisors; the others are 1, 2, 6, 12, 60, and 2520 (sequence A072938 in the OEIS).

• 360 is also a
  decimal since the sum of its digits (9
  ) is a divisor of 360.

• 360 is divisible by the number of its divisors (
  7. Furthermore, one of the divisors of 360 is 72, which is the number of primes
  below it.

• 360 is the sum of twin primes (179 + 181) and the sum of four consecutive powers of three (9 + 27 + 81 + 243).

• The sum of Euler's totient function φ(x) over the first thirty-four integers is 360.

• 360 is a triangular matchstick number.^[2]

• 360 is the product of the first two unitary perfect numbers:^[3] ${\displaystyle 60\times 6=360.}$

• There are 360 even permutations of 6 elements. They form the alternating group A₆.

A

${\displaystyle 361=19^{2},}$ centered triangular number,[4] centered octagonal number, centered decagonal number,^[5] member of the Mian–Chowla sequence;^[6] also the number of positions on a standard 19 × 19 Go board.

362

${\displaystyle 362=2\times 181=\sigma _{2}(19)}$: sum of squares of divisors of 19,^[7] Mertens function returns 0,^[8] nontotient, noncototient.^[9]

363

364

${\displaystyle 364=2^{2}\times 7\times 13}$, tetrahedral number,^[10] sum of twelve consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), Mertens function returns 0,^[11] nontotient.

It is a

366

${\displaystyle 366=2\times 3\times 61,}$ sphenic number,^[13] Mertens function returns 0,^[14] noncototient,^[15] number of complete partitions of 20,^[16] 26-gonal and 123-gonal. There are also 366 days in a leap year.

367

367 is a prime number, Perrin number,^[17] happy number, prime index prime and a strictly non-palindromic number.

368

${\displaystyle 368=2^{4}\times 23.}$ It is also a Leyland number.^[18]

369

References

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Sources

• Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers (p. 152). London: Penguin Group.

External links

• Media related to 360 (number) at Wikimedia Commons