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

1,7

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A369053 A340328 A271076 * A188817 A271099 A344259

Adjacent sequences: A087172 A087173 A087174 * A087176 A087177 A087178

Keyword

nonn

Author

Reinhard Zumkeller, Aug 23 2003

Status

approved