A260233 - OEIS

%I #8 May 05 2016 10:34:34

%S 2,3,2,3,2,7,2,3,2,3,2,5,2,3,2,3,2,19,2,3,2,3,2,5,2,3,2,3,2,31,2,3,2,

%T 3,2,37,2,3,2,3,2,5,2,3,2,3,2,7,2,3,2,3,2,5,2,3,2,3,2,11,2,3,2,3,2,7,

%U 2,3,2,3,2,5,2,3,2,3,2,79,2,3,2,3,2,5,2

%N Smallest prime factor of the n-th hexagonal number (A000384).

%H Colin Barker, <a href="/A260233/b260233.txt">Table of n, a(n) for n = 2..1000</a>

%F a(n) = A020639(A000384(n)).

%e a(3) = 3 because A000384(3) = 15 = 3 * 5.

%t Table[FactorInteger[n(2n-1)][[1,1]],{n,2,100}] (* _Harvey P. Dale_, May 05 2016 *)

%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(6, n))

%Y Cf. A000384, A020639, A260234, A260235, A260236.

%K nonn

%O 2,1

%A _Colin Barker_, Jul 20 2015