116 (number)

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← 115 116 117 →
Cardinal one hundred sixteen
Ordinal 116th
(one hundred sixteenth)
Factorization 22 × 29
Divisors 1, 2, 4, 29, 58, 116
Greek numeral ΡΙϚ´
Roman numeral CXVI, cxvi
Binary 11101002
Ternary 110223
Senary 3126
Octal 1648
Duodecimal 9812
Hexadecimal 7416

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

Contents

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.). "SequenceA005278(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.). "SequenceA002981(Numbers n such that n! + 1 is prime)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation..
  3. ↑ Sloane, N. J. A. (ed.). "SequenceA027376(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.). "SequenceA007052(Number of order-consecutive partitions of n)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation..
  5. ↑ Sloane, N. J. A. (ed.). "SequenceA008404(Number of Costas arrays of order n, counting rotations and flips as distinct)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation..
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