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Number of prime factors, with multiplicity, of the n-th pentagonal number (A000326).
4

%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