360 (number)
| ||||
---|---|---|---|---|
Cardinal | three hundred sixty | |||
Ordinal | 360th (three hundred sixtieth) | |||
Factorization | 23 × 32 × 5 | |||
Divisors | 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360 | |||
Greek numeral | ||||
Roman numeral | CCCLX | |||
Binary | 1011010002 | |||
Ternary | 1111003 | |||
Senary | 14006 | |||
Octal | 5508 | |||
Duodecimal | 26012 | |||
Hexadecimal | 16816 |
360 (three hundred [and] sixty) is the natural number following 359 and preceding 361.
In mathematics[edit]
- 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 superior highly composite number, a colossally abundant number, 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.[2]
- 360 is the product of the first two unitary perfect numbers:[3]
- There are 360 even permutations of 6 elements. They form the alternating group A6.
A circle is divided into 360 degrees for angular measurement. 360° = 2
Integers from 361 to 369[edit]
361[edit]
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[edit]
: sum of squares of divisors of 19,[7] Mertens function returns 0,[8] nontotient, noncototient.[9]
363[edit]
364[edit]
, 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 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.[12]
365[edit]
366[edit]
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[edit]
367 is a prime number, Perrin number,[17] happy number, prime index prime and a strictly non-palindromic number.
368[edit]
It is also a Leyland number.[18]
369[edit]
References[edit]
- ^ Sloane, N. J. A. (ed.). "Sequence A002182 (Highly composite numbers, definition (1): numbers n where d(n), the number of divisors of n (A000005), increases to a record.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A045943 (Triangular matchstick numbers: a(n) is 3*n*(n+1)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002827 (Unitary perfect numbers: numbers k such that usigma(k) - k equals k.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-02.
- ^ "Centered Triangular Number". mathworld.wolfram.com.
- ^ Sloane, N. J. A. (ed.). "Sequence A062786 (Centered 10-gonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-22.
- ^ Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-22.
- ^ Sloane, N. J. A. (ed.). "Sequence A001157 (a(n) = sigma_2(n): sum of squares of divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A028442 (Numbers k such that Mertens's function M(k) (A002321) is zero)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Noncototient". mathworld.wolfram.com.
- ^ Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-22.
- ^ Sloane, N. J. A. (ed.). "Sequence A028442 (Numbers k such that Mertens's function M(k) (A002321) is zero)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral (or triangular pyramidal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sphenic number". mathworld.wolfram.com.
- ^ Sloane, N. J. A. (ed.). "Sequence A028442 (Numbers k such that Mertens's function M(k) (A002321) is zero)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Noncototient". mathworld.wolfram.com.
- ^ Sloane, N. J. A. (ed.). "Sequence A126796 (Number of complete partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Parrin number". mathworld.wolfram.com.
- ^ Sloane, N. J. A. (ed.). "Sequence A076980". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
This article includes a list of general references, but it lacks sufficient corresponding inline citations. (April 2011) |
Sources[edit]
- Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers (p. 152). London: Penguin Group.
External links[edit]
- Media related to 360 (number) at Wikimedia Commons