360 (number)

From HandWiki
Short description: Natural number
← 359 360 361 →
Cardinalthree hundred sixty
Ordinal360th
(three hundred sixtieth)
Factorization23 × 32 × 5
Divisors1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
Greek numeralΤΞ´
Roman numeralCCCLX
Binary1011010002
Ternary1111003
Quaternary112204
Quinary24205
Senary14006
Octal5508
Duodecimal26012
Hexadecimal16816
VigesimalI020
Base 36A036

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

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 the smallest number with exactly 24 divisors, 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 a triangular matchstick number.[2]

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

A circle is divided into 360 degrees for angular measurement. 360° = 2π rad 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]\displaystyle{ 361=19^2, }[/math] 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

[math]\displaystyle{ 362=2\times181=\sigma_2(19) }[/math]: sum of squares of divisors of 19,[7] Mertens function returns 0,[8] nontotient, noncototient.[9]

363

Main page: 363 (number)

364

[math]\displaystyle{ 364=2^2\times 7\times 13 }[/math], 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

Main page: 365 (number)

366

[math]\displaystyle{ 366=2\times 3\times 61, }[/math] 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

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

369

Main page: 369 (number)

References

  1. ↑ 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.)". OEIS Foundation. https://oeis.org/A002182. Retrieved 2016-05-31. 
  2. ↑ Sloane, N. J. A., ed. "Sequence A045943 (Triangular matchstick numbers: a(n) is 3*n*(n+1)/2)". OEIS Foundation. https://oeis.org/A045943. 
  3. ↑ Sloane, N. J. A., ed. "Sequence A002827 (Unitary perfect numbers: numbers k such that usigma(k) - k equals k.)". OEIS Foundation. https://oeis.org/A002827. Retrieved 2023-11-02. 
  4. ↑ "Centered Triangular Number". https://mathworld.wolfram.com/CenteredTriangularNumber.html. 
  5. ↑ Sloane, N. J. A., ed. "Sequence A062786 (Centered 10-gonal numbers)". OEIS Foundation. https://oeis.org/A062786. Retrieved 2016-05-22. 
  6. ↑ Sloane, N. J. A., ed. "Sequence A005282 (Mian-Chowla sequence)". OEIS Foundation. https://oeis.org/A005282. Retrieved 2016-05-22. 
  7. ↑ Sloane, N. J. A., ed. "Sequence A001157 (a(n) = sigma_2(n): sum of squares of divisors of n)". OEIS Foundation. https://oeis.org/A001157. 
  8. ↑ Sloane, N. J. A., ed. "Sequence A028442 (Numbers k such that Mertens's function M(k) (A002321) is zero)". OEIS Foundation. https://oeis.org/A028442. 
  9. ↑ "Noncototient". https://mathworld.wolfram.com/Noncototient.html. 
  10. ↑ Sloane, N. J. A., ed. "Sequence A000292 (Tetrahedral numbers)". OEIS Foundation. https://oeis.org/A000292. Retrieved 2016-05-22. 
  11. ↑ Sloane, N. J. A., ed. "Sequence A028442 (Numbers k such that Mertens's function M(k) (A002321) is zero)". OEIS Foundation. https://oeis.org/A028442. 
  12. ↑ Sloane, N. J. A., ed. "Sequence A000292 (Tetrahedral (or triangular pyramidal) numbers)". OEIS Foundation. https://oeis.org/A000292. 
  13. ↑ "Sphenic number". https://mathworld.wolfram.com/SphenicNumber.html. 
  14. ↑ Sloane, N. J. A., ed. "Sequence A028442 (Numbers k such that Mertens's function M(k) (A002321) is zero)". OEIS Foundation. https://oeis.org/A028442. 
  15. ↑ "Noncototient". https://mathworld.wolfram.com/Noncototient.html. 
  16. ↑ Sloane, N. J. A., ed. "Sequence A126796 (Number of complete partitions of n)". OEIS Foundation. https://oeis.org/A126796. 
  17. ↑ "Parrin number". https://mathworld.wolfram.com/PerrinSequence.html. 
  18. ↑ Sloane, N. J. A., ed. "Sequence A076980". OEIS Foundation. https://oeis.org/A076980. 

Sources

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

External links



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