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116 (number)

From Wikipedia, the free encyclopedia
"One hundred sixteen" redirects here. For other uses, see116 (disambiguation).
Natural number
← 115116 117 →
Cardinalone hundred sixteen
Ordinal116th
(one hundred sixteenth)
Factorization22 × 29
Divisors1, 2, 4, 29, 58, 116
Greek numeralΡΙϚ´
Roman numeralCXVI,cxvi
Binary11101002
Ternary110223
Senary3126
Octal1648
Duodecimal9812
Hexadecimal7416

116 (one hundred [and] sixteen) is thenatural number following115 and preceding117.

In mathematics

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116 is anoncototient, meaning that there is no solution to the equationmφ(m) =n, whereφ stands forEuler's totient function.[1]

116! + 1 is afactorial prime.[2]

There are 116 ternaryLyndon words of length six, and 116irreducible polynomials of degree six over a three-element field, which form the basis of afree 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 everyk, the union of the firstk subsets is a consecutive sequence of integers.[4]

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

See also

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References

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  1. ^Sloane, N. J. A. (ed.)."Sequence A005278 (Noncototients: n such that x-phi(x)=n has no solution)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation..
  2. ^Sloane, N. J. A. (ed.)."Sequence A002981 (Numbers n such that n! + 1 is prime)".TheOn-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)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation..
  4. ^Sloane, N. J. A. (ed.)."Sequence A007052 (Number of order-consecutive partitions of n)".TheOn-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)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation..
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