A181186 Number of prime factors of (2^n - 1) * n! + 1, counted with multiplicity.

1, 1, 1, 2, 2, 1, 3, 3, 2, 2, 3, 2, 3, 5, 3, 2, 1, 3, 2, 2, 3, 3, 2, 6, 1, 4, 4, 3, 3, 3, 2, 2, 4, 3, 5, 2, 4, 2, 4, 1, 4, 4, 3, 3, 1, 3, 4, 5, 3, 4, 4, 5, 2, 2, 2, 6, 4, 2, 5, 3, 7, 4, 3, 2, 5, 3, 4, 4, 4, 2, 7, 6, 7, 3, 5, 2, 4, 3, 8, 8, 6, 4

Offset: 1

Author

Jason Earls, Oct 09 2010

Keywords

• nonn

Comments

a(101) >= 3. See link to factordb.com. - Hugo Pfoertner, Aug 07 2019

Links

• Yurii Ivanov, Table of n, a(n) for n = 1..103 (terms 1..100 from Sean A. Irvine and Hugo Pfoertner, term 101 from Tyler Busby)
• Sean A. Irvine, Factorizations of (2^n-1)*n!+1
• factordb.com, Status of (2^n-1)*n!+1.

Crossrefs

Cf. A001222, A052589.

Programs

Mathematica

Table[PrimeOmega[(2^n-1)n!+1],{n,90}] (* The program takes a long time to run. *) (* Harvey P. Dale, Feb 10 2019 *)

Formula

a(n) = A001222(A052589(n)+1). - Michel Marcus, Apr 08 2023

Extensions

More terms from Sean A. Irvine, Sep 15 2012