"One hundred sixteen" redirects here. For other uses, see 116 (disambiguation).

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

References

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