A048858 Number of prime factors of 1+(n!)^2 (with multiplicity).

1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 3, 2, 2, 2, 2, 2, 5, 3, 4, 3, 1, 3, 5, 7, 2, 2, 6, 4, 4, 5, 4, 3, 3, 3, 4, 4, 4, 2, 5, 5, 7, 2, 3, 8, 9, 3, 3, 4, 3, 2, 4, 2, 8, 6, 4, 3, 8, 2, 5, 4, 5, 1, 5, 5, 4, 5, 4

Offset: 0

Author

Charles T. Le (charlestle(AT)yahoo.com)

Keywords

• nonn
• more

Links

• H. Ibstedt, A Few Smarandache Integer Sequences, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, pp. 171-183.

Crossrefs

Cf. A001222, A020549.

Programs

Mathematica

Table[Length[FactorInteger[1 + (n!)^2]], {n, 0, 20}] (* T. D. Noe, Oct 17 2011 *)
PrimeOmega[1+(Range[0,20]!)^2] (* Harvey P. Dale, Dec 28 2024 *)

PARI

a(n)=bigomega(n!^2+1) \\ Charles R Greathouse IV, Sep 20 2012

Formula

a(n) = A001222(A020549(n)). - Michel Marcus, Aug 09 2021

Extensions

Corrected by Arkadiusz Wesolowski, Oct 17 2011

Corrected by Charles R Greathouse IV, Sep 20 2012

a(38)-a(54) from Giovanni Resta, Jun 26 2018

a(55)-a(61) from Jinyuan Wang, Aug 09 2021

a(62)-a(70) from Sean A. Irvine, Sep 30 2021