A066835 a(n) = omega((prime(n)-1)! + 1), where omega is given by A001221, primes in A000040.

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

Offset

1,4

Links

Table of n, a(n) for n=1..34.

Hisanori Mishima, Appendix 1. Factorization results for n!+1

Eric Weisstein's World of Mathematics, Wilson's Theorem

Formula

a(n) = A066856(A006093(n)). - Jinyuan Wang, Apr 01 2020

Example

a(7) = omega(prime(7)-1)! + 1) = omega((17-1)! + 1) = omega(16! + 1) = omega(2092278988800 + 1) = omega(2092278988801) = 5, as 2092278988801 = 17 * 61 * 137 * 139 * 1059511 = prime(7)*prime(18)*prime(33)*prime(34)*prime(82801).

Mathematica

Table[ Length[ FactorInteger[ (Prime[ n ] - 1)! + 1 ] ], {n, 1, 15} ]

Prog

(PARI) a(n) = omega((prime(n)-1)! + 1); \\ Jinyuan Wang, Apr 01 2020

Crossrefs

Cf. A000040, A000142, A001221, A006093, A066856.

Sequence in context: A073819 A190846 A214787 * A123953 A097006 A033306

Adjacent sequences: A066832 A066833 A066834 * A066836 A066837 A066838

Keyword

nonn,more

Author

Reinhard Zumkeller, Jan 20 2002

Extensions

More terms from Robert G. Wilson v, Jan 21 2002

a(27)-a(34) from Jinyuan Wang, Apr 01 2020

Status

approved