360 (number)

File:Compound of five cubes, gray and rgby.png

The surface of the compound of five cubes consists of 360 triangles.

360 (three hundred [and] sixty) is the natural number following 359 and preceding 361.

In mathematics

• 360 is the 13th highly composite number<ref>Template:Cite OEIS</ref> 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 Template:OEIS.

• 360 is also the 6th superior highly composite number,<ref>Template:Cite web</ref> the 6th colossally abundant number,<ref>Template:Cite web</ref> a refactorable number, a 5-smooth number, and a Harshad number in decimal since the sum of its digits (9) is a divisor of 360.

• 360 is divisible by the number of its divisors (24), and it is the smallest number divisible by every natural number from 1 to 10, except 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.<ref>Template:Cite OEIS</ref>

• 360 is the product of the first two unitary perfect numbers:<ref>Template:Cite OEIS</ref> <math>60 \times 6 = 360.</math>

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

A turn is divided into 360 degrees for angular measurement. Template:Math is also called a round angle. This unit choice divides round angles into equal sectors measured in integer rather than fractional degrees. Many angles commonly appearing in planimetrics have an integer number of degrees. For a simple non-intersecting polygon, the sum of the internal angles of a quadrilateral always equals 360 degrees.

Integers from 361 to 369

361

<math>361=19^2,</math> centered triangular number,<ref>Template:Cite web</ref> centered octagonal number, centered decagonal number,<ref>Template:Cite OEIS</ref> member of the Mian–Chowla sequence.<ref>Template:Cite OEIS</ref> There are also 361 positions on a standard 19 × 19 Go board.

362

<math>362=2\times181=\sigma_2(19)</math>: sum of squares of divisors of 19,<ref>Template:Cite OEIS</ref> Mertens function returns 0,<ref name="auto">Template:Cite OEIS</ref> nontotient, noncototient.<ref name="auto1">Template:Cite web</ref>

364

<math>364=2^2\times 7\times 13</math>, tetrahedral number,<ref>Template:Cite OEIS</ref> sum of twelve consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), Mertens function returns 0,<ref name="auto"/> nontotient.

It is a repdigit in bases three (111111), nine (444), twenty-five (EE), twenty-seven (DD), fifty-one (77), and ninety (44); the sum of six consecutive powers of three (1 + 3 + 9 + 27 + 81 + 243); and the twelfth non-zero tetrahedral number.<ref>Template:Cite OEIS</ref>

365

Template:Main 365 is the amount of days in a common year. For the common year, see common year.

366

<math>366=2\times 3\times 61,</math> sphenic number,<ref>Template:Cite web</ref> Mertens function returns 0,<ref name="auto"/> noncototient,<ref name="auto1"/> number of complete partitions of 20,<ref>Template:Cite OEIS</ref> 26-gonal and 123-gonal. There are also 366 days in a leap year.

367

367 is a prime number, Perrin number,<ref>Template:Cite web</ref> happy number, prime index prime and a strictly non-palindromic number.

368

<math>368=2^4\times 23.</math> It is also a Leyland number.<ref>Template:Cite OEIS</ref>

Sources

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

External links

• Template:Commons category-inline