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%I #15 Dec 28 2017 14:32:57
%S 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,
%T 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,
%U 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
%N Number of distinct primes dividing the n-th partition number.
%H Giovanni Resta, <a href="/A087175/b087175.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PartitionFunction.html">Partition Function</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Partition_(number_theory)">Partition function</a>
%F a(n) = A001221(A000041(n)).
%e A000041(14) = 135 = 3^3 * 5, so a(14) = 2.
%e A000041(97) = 133230930 = 2*3*5*7*29*131*167, so a(97)=7.
%t Table[If[n==1,0,Length[FactorInteger[PartitionsP[n]]]],{n,1,100}] (* _Jonathan Sondow_, Aug 19 2011 *)
%o (PARI) a(n)={omega(numbpart(n))} \\ _Andrew Howroyd_, Dec 28 2017
%Y Cf. A000041, A001221, A085561. See also A071963, A192885.
%K nonn
%O 1,7
%A _Reinhard Zumkeller_, Aug 23 2003