A085561 - OEIS

%I #17 Dec 28 2017 14:31:34

%S 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,

%T 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,

%U 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

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

%H Giovanni Resta, <a href="/A085561/b085561.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A001222(A000041(n)). - _Andrew Howroyd_, Dec 28 2017

%p 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

%t PrimeOmega[PartitionsP[Range[0,110]]] (* _Harvey P. Dale_, Dec 26 2014 *)

%o (PARI) a(n)={bigomega(numbpart(n))} \\ _Andrew Howroyd_, Dec 28 2017

%Y Cf. A001222, A000041.

%K nonn

%O 0,8

%A _Jason Earls_, Jul 05 2003