116 (number)

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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
Binary 11101002
Ternary 110223
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

Related Research Articles

222 is the natural number following 221 and preceding 223.

86 (eighty-six) is the natural number following 85 and preceding 87.

34 (thirty-four) is the natural number following 33 and preceding 35.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

300 is the natural number following 299 and preceding 301.

400 is the natural number following 399 and preceding 401.

500 is the natural number following 499 and preceding 501.

700 is the natural number following 699 and preceding 701.

600 is the natural number following 599 and preceding 601.

800 is the natural number following 799 and preceding 801.

900 is the natural number following 899 and preceding 901. It is the square of 30 and the sum of Euler's totient function for the first 54 positive integers. In base 10 it is a Harshad number.

2000 is a natural number following 1999 and preceding 2001.

100,000 (one hundred thousand) is the natural number following 99,999 and preceding 100,001. In scientific notation, it is written as 105.

162 is the natural number between 161 and 163.

501 is the natural number following 500 and preceding 502.

270 is the natural number following 269 and preceding 271.

290 is the natural number following 289 and preceding 291.

204 is the natural number following 203 and preceding 205.

232 is the natural number following 231 and preceding 233.

Bell triangle

In mathematics, the Bell triangle is a triangle of numbers analogous to Pascal's triangle, whose values count partitions of a set in which a given element is the largest singleton. It is named for its close connection to the Bell numbers, which may be found on both sides of the triangle, and which are in turn named after Eric Temple Bell. The Bell triangle has been discovered independently by multiple authors, beginning with Charles Sanders Peirce (1880) and including also Alexander Aitken (1933) and Cohn et al. (1962), and for that reason has also been called Aitken's array or the Peirce triangle.

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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