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

0,8

Links

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

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A001222, A000041.

Sequence in context: A357633 A322997 A367315 * A260651 A116370 A261018

Adjacent sequences: A085558 A085559 A085560 * A085562 A085563 A085564

Keyword

nonn

Author

Jason Earls, Jul 05 2003

Status

approved