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%I #5 Jul 03 2015 07:45:23
%S 0,1,2,2,2,2,3,2,2,2,2,4,2,2,4,2,2,2,3,3,3,3,3,3,2,3,3,3,2,3,3,3,3,2,
%T 4,3,3,2,4,4,2,3,2,3,3,2,4,4,2,2,4,4,2,3,4,3,4,2,3,4,3,3,4,2,3,3,3,4,
%U 3,4,3,4,2,3,4,3,4,3,3,3,2,3,3,4,3,2
%N Number of distinct prime factors of the n-th pentagonal number (A000326).
%H Colin Barker, <a href="/A259651/b259651.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A001221(A000326(n)).
%e a(3) = 2 because A000326(3) = 12 = 2^2 * 3.
%o (PARI)
%o pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
%o a(n) = omega(pg(5, n))
%Y Cf. A000326, A001221, A259649, A259650, A259652.
%K nonn
%O 1,3
%A _Colin Barker_, Jul 02 2015
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