116 (number)

116 (one hundred [and] sixteen) is the natural number following 115 and preceding 117.
116 Cardinal one hundred [and] sixteen Ordinal 116th
(one hundred [and] sixteenth)Numeral system 114 Factorization Divisors 1, 2, 4, 29, 58, 116 Roman numeral CXVI Binary 1110100_{2} Octal 164_{8} Duodecimal 98_{12} Hexadecimal 74_{16} 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 prime.^{[2]} There are 116 ternary Lyndon words of length six, and 116 irreducible polynomials of degree six over a threeelement 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]}
In other fields
One hundred sixteen is also:
 The prefix for several EUwide telephone helplines designated as harmonised service of social value
 The atomic number of an element temporarily called ununhexium
 The number of years that the Hundred Years' War between France and England, from 1337 to 1453, actually lasted
 The fire emergency telephone number in Peru
 The record for number of wins in a single season of Major League Baseball achieved by the Chicago Cubs in 1906 and the Seattle Mariners in 2001.
 The number of pages in the Lost 116 pages, the original manuscript of what Joseph Smith, Jr. said was the translation of the Book of Lehi, of the Golden plates revealed to him in 1827
See also
 List of highways numbered 116
 National longevity recordholders
 Oldest people
 116th Street (Manhattan)
 116th Street Crew, a mafia crew named after the Manhattan street
 The 116 Clique, a group of Christian rappers from Dallas, TX named after the Bible verse Romans 1:16
References
 ^ Sloane's A005278 : Noncototients: n such that xphi(x)=n has no solution. The OnLine Encyclopedia of Integer Sequences. OEIS Foundation..
 ^ Sloane's A002981 : Numbers n such that n! + 1 is prime. The OnLine Encyclopedia of Integer Sequences. OEIS Foundation..
 ^ Sloane's A027376 : Number of ternary irreducible polynomials of degree n; dimensions of free Lie algebras. The OnLine Encyclopedia of Integer Sequences. OEIS Foundation..
 ^ Sloane's A007052 : Number of orderconsecutive partitions of n. The OnLine Encyclopedia of Integer Sequences. OEIS Foundation..
 ^ Sloane's A008404 : Number of Costas arrays of order n, counting rotations and flips as distinct. The OnLine Encyclopedia of Integer Sequences. OEIS Foundation..
Categories: Integers
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