A260233 Smallest prime factor of the n-th hexagonal number (A000384).

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, 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, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 79, 2, 3, 2, 3, 2, 5, 2

Offset: 2

Author

Colin Barker, Jul 20 2015

Keywords

• nonn

Examples

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

Links

• Colin Barker, Table of n, a(n) for n = 2..1000

Crossrefs

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

Programs

Mathematica

Table[FactorInteger[n(2n-1)][[1,1]],{n,2,100}] (* Harvey P. Dale, May 05 2016 *)

PARI

pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
spf(m) = factorint(m)[1,1] \\ Smallest prime factor
a(n) = spf(pg(6, n))

Formula

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