OFFSET
1,2
COMMENTS
If a(n) = 2, then n is in A006549 (Mersenne-primes, Fermat-primes-1).
If a(n) = 2, then n is in A006549, being either a Mersenne prime, a Fermat prime minus one, or n=8, corresponding to the unique solution to Catalan's equation, 3^2 = 2^3 + 1. - Gene Ward Smith, Sep 07 2006
a(n-1), n > 2, is the number of maximal subsemigroups of the monoid of orientation-preserving partial injective mappings on a set with n elements. - Wilf A. Wilson, Jul 21 2017
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
James East, Jitender Kumar, James D. Mitchell, and Wilf A. Wilson, Maximal subsemigroups of finite transformation and partition monoids, arXiv:1706.04967 [math.GR], 2017. [Wilf A. Wilson, Jul 21 2017]
FORMULA
EXAMPLE
For n = 30030, n has 6 prime factors, 30031 = 59*509 so a(30030) = 6+2 = 8.
For n = 30029, a(30029) = 1+6 = 7.
MATHEMATICA
Table[ PrimeNu[n*(n + 1)], {n, 1, 100}] (* G. C. Greubel, May 13 2017 *)
PROG
(PARI) for(n=1, 100, print1(omega(n*(n+1)), ", ")) \\ G. C. Greubel, May 13 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Labos Elemer, Mar 02 2001
EXTENSIONS
Name corrected by Rick L. Shepherd, Apr 11 2023
STATUS
approved