A087175 Number of distinct primes dividing the n-th partition number.

0, 1, 1, 1, 1, 1, 2, 2, 3, 3, 2, 2, 1, 2, 2, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 4, 4, 4, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 5, 3, 5, 4, 3, 3, 4, 5, 3, 5, 4, 3, 5, 2, 4, 2, 4, 3, 4, 3, 3, 3, 4, 6, 2, 1, 4, 4, 4, 2, 4, 3, 5, 2, 5, 2, 4, 3, 2, 3, 2, 2, 6, 2, 4, 7, 3, 2, 5, 3, 3

Offset: 1

Author

Reinhard Zumkeller, Aug 23 2003

Keywords

• nonn

Examples

			A000041(14) = 135 = 3^3 * 5, so a(14) = 2.
A000041(97) = 133230930 = 2*3*5*7*29*131*167, so a(97)=7.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Distinct Prime Factors
• Eric Weisstein's World of Mathematics, Partition Function
• Wikipedia, Partition function

Crossrefs

Cf. A000041, A001221, A085561. See also A071963, A192885.

Programs

Mathematica

Table[If[n==1,0,Length[FactorInteger[PartitionsP[n]]]],{n,1,100}] (* Jonathan Sondow, Aug 19 2011 *)

PARI

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

Formula

a(n) = A001221(A000041(n)).