A066877 a(n) = omega(n!-1), where omega is the number of distinct primes dividing n, A001221.

0, 0, 1, 1, 2, 1, 1, 2, 2, 2, 4, 1, 2, 1, 4, 2, 3, 3, 3, 2, 4, 3, 2, 2, 3, 2, 2, 4, 5, 1, 3, 1, 1, 2, 3, 2, 5, 1, 4, 2, 4, 4, 7, 4, 5, 5, 2, 4, 3, 2, 5, 5, 4, 6, 6, 5, 6, 5, 2, 3, 4, 4, 5, 4, 6, 4, 7, 2, 6, 5, 5, 3, 4, 5, 7, 3, 5, 4, 2, 4, 4, 4, 4, 6, 2, 3, 4

Offset: 1

Author

Robert G. Wilson v, Jan 21 2002

Keywords

• hard
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..135
• Hisanori Mishima, Appendix 1. Factorization results for n!-1

Programs

Mathematica

Table[ Length[ FactorInteger[ n! - 1]], {n, 1, 30}]

Extensions

a(52) corrected and more terms added by Amiram Eldar, Oct 03 2019