A259649 - OEIS

%I #6 Jul 03 2015 07:42:35

%S 5,2,2,5,3,2,2,3,5,2,2,13,7,2,2,5,3,2,2,3,5,2,2,5,7,2,2,29,3,2,2,3,17,

%T 2,2,5,19,2,2,41,3,2,2,3,23,2,2,7,5,2,2,53,3,2,2,3,29,2,2,7,5,2,2,5,3,

%U 2,2,3,5,2,2,73,13,2,2,5,3,2,2,3,5,2,2

%N Smallest prime factor of the n-th pentagonal number (A000326).

%H Colin Barker, <a href="/A259649/b259649.txt">Table of n, a(n) for n = 2..1000</a>

%F a(n) = A020639(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 spf(m) = factorint(m)[1,1] \\ Smallest prime factor

%o a(n) = spf(pg(5, n))

%Y Cf. A000326, A020639, A259650, A259651, A259652.

%K nonn

%O 2,1

%A _Colin Barker_, Jul 02 2015