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

Author

Reinhard Zumkeller, Jan 20 2002

Keywords

• nonn
• more
• hard

Examples

			a(7) = omega((prime(7)-1)! + 1) = omega((17-1)! + 1) = omega(16! + 1) = omega(20922789888000 + 1) = omega(20922789888001) = 5, as 20922789888001 = 17 * 61 * 137 * 139 * 1059511 = prime(7)*prime(18)*prime(33)*prime(34)*prime(82801).
		

Links

• Hisanori Mishima, Appendix 1. Factorization results for n!+1
• Eric Weisstein's World of Mathematics, Wilson's Theorem

Crossrefs

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

Programs

Mathematica

Table[ Length[ FactorInteger[ (Prime[ n ] - 1)! + 1 ] ], {n, 1, 15} ]
PrimeNu[(Prime[Range[15]] - 1)! + 1] (* Paolo Xausa, Feb 07 2025 *)

PARI

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

Formula

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

Extensions

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

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