A085561 Number of prime divisors of the partition numbers (counted with multiplicity).

0, 0, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 2, 1, 4, 5, 3, 4, 3, 4, 3, 6, 3, 2, 5, 3, 5, 4, 4, 3, 4, 3, 4, 5, 3, 4, 1, 3, 4, 7, 5, 4, 3, 6, 4, 3, 4, 5, 3, 4, 3, 4, 5, 4, 5, 5, 3, 3, 5, 6, 3, 5, 5, 3, 5, 2, 9, 2, 5, 3, 8, 3, 3, 3, 7, 8, 2, 1, 5, 5, 6, 2, 6, 3, 6, 3, 5, 2, 5, 5, 2, 3, 2, 2, 8, 2, 15, 7, 5, 4, 6, 3, 3, 5, 4

Offset: 0

Author

Jason Earls, Jul 05 2003

Keywords

• nonn

Links

• Giovanni Resta, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001222, A000041.

Programs

Maple

with(numtheory):with(combinat):a:=proc(n) if n=0 then 0 else bigomega(numbpart(n)) fi end: seq(a(n), n=0..104); # Zerinvary Lajos, Apr 11 2008

Mathematica

PrimeOmega[PartitionsP[Range[0,110]]] (* Harvey P. Dale, Dec 26 2014 *)

PARI

a(n)={bigomega(numbpart(n))} \\ Andrew Howroyd, Dec 28 2017

Formula

a(n) = A001222(A000041(n)). - Andrew Howroyd, Dec 28 2017