116 (number)

From HandWiki
Short description: Natural number
← 115 116 117 →
Cardinalone hundred sixteen
Ordinal116th
(one hundred sixteenth)
Factorization22 × 29
Divisors1, 2, 4, 29, 58, 116
Greek numeralΡΙϚ´
Roman numeralCXVI
Binary11101002
Ternary110223
Quaternary13104
Quinary4315
Senary3126
Octal1648
Duodecimal9812
Hexadecimal7416
Vigesimal5G20
Base 363836

116 (one hundred [and] sixteen) is the natural number following 115 and preceding 117.

In mathematics

116 is a noncototient, meaning that there is no solution to the equation m − φ(m) = n, where φ stands for Euler's totient function.[1]

116! + 1 is a factorial prime.[2]

There are 116 ternary Lyndon words of length six, and 116 irreducible polynomials of degree six over a three-element field, which form the basis of a free Lie algebra of dimension 116.[3]

There are 116 different ways of partitioning the numbers from 1 through 5 into subsets in such a way that, for every k, the union of the first k subsets is a consecutive sequence of integers.[4]

There are 116 different 6×6 Costas arrays.[5]

See also

  • 116 (disambiguation)

References

  1. ↑ Sloane, N. J. A., ed. "Sequence A005278 (Noncototients: n such that x-phi(x)=n has no solution)". OEIS Foundation. https://oeis.org/A005278. .
  2. ↑ Sloane, N. J. A., ed. "Sequence A002981 (Numbers n such that n! + 1 is prime)". OEIS Foundation. https://oeis.org/A002981. .
  3. ↑ Sloane, N. J. A., ed. "Sequence A027376 (Number of ternary irreducible polynomials of degree n; dimensions of free Lie algebras)". OEIS Foundation. https://oeis.org/A027376. .
  4. ↑ Sloane, N. J. A., ed. "Sequence A007052 (Number of order-consecutive partitions of n)". OEIS Foundation. https://oeis.org/A007052. .
  5. ↑ Sloane, N. J. A., ed. "Sequence A008404 (Number of Costas arrays of order n, counting rotations and flips as distinct)". OEIS Foundation. https://oeis.org/A008404. .



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