%I #8 Jul 22 2015 08:46:13
%S 0,1,3,2,2,2,3,3,3,2,5,4,2,2,4,4,3,3,4,3,3,3,3,4,3,3,7,3,2,3,3,6,4,2,
%T 5,4,3,2,4,5,2,5,7,3,4,2,4,6,3,3,5,4,2,5,4,4,4,2,5,4,3,3,5,6,3,3,5,4,
%U 3,4,3,6,2,3,8,3,4,3,3,5,6,4,4,4,3,2
%N Number of prime factors, with multiplicity, of the n-th pentagonal number (A000326).
%H Colin Barker, <a href="/A259652/b259652.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A001222(A000326(n)).
%e a(3) = 3 because A000326(3) = 12 = 2 * 2 * 3.
%t Table[PrimeOmega[n*(3n-1)/2],{n,100}] (* _Harvey P. Dale_, Jul 22 2015 *)
%o (PARI)
%o pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
%o a(n) = bigomega(pg(5, n))
%Y Cf. A000326, A001222, A259649, A259650, A259651.
%K nonn
%O 1,3
%A _Colin Barker_, Jul 02 2015