World Library  
Flag as Inappropriate
Email this Article

116 (number)

Article Id: WHEBN0000498596
Reproduction Date:

Title: 116 (number)  
Author: World Heritage Encyclopedia
Language: English
Subject: 115 (number), 111 (number), 114 (number), Noncototient, Integers
Collection: Integers
Publisher: World Heritage Encyclopedia

116 (number)

115 116 117
Cardinal one hundred sixteen
Ordinal 116th
(one hundred and sixteenth)
Factorization 22× 29
Divisors 1, 2, 4, 29, 58, 116
Roman numeral CXVI
Binary 11101002
Ternary 110223
Quaternary 13104
Quinary 4315
Senary 3126
Octal 1648
Duodecimal 9812
Hexadecimal 7416
Vigesimal 5G20
Base 36 3836

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


  • In mathematics 1
  • In other fields 2
  • See also 3
  • References 4

In mathematics

116 is a noncototient, meaning that there is no solution to the equation mφ(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 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]

In other fields

One hundred sixteen is also:

See also


  1. ^ "Sloane's A005278 : Noncototients: n such that x-phi(x)=n has no solution", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..
  2. ^ "Sloane's A002981 : Numbers n such that n! + 1 is prime", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..
  3. ^ "Sloane's 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's A007052 : Number of order-consecutive partitions of n", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..
  5. ^ "Sloane's A008404 : Number of Costas arrays of order n, counting rotations and flips as distinct", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.