A271321 Smallest prime factor of the n-th n-gonal number (A060354).

2, 2, 2, 5, 2, 2, 2, 3, 2, 2, 2, 13, 2, 2, 2, 11, 2, 2, 2, 3, 2, 2, 2, 5, 2, 2, 2, 29, 2, 2, 2, 3, 2, 2, 2, 37, 2, 2, 2, 11, 2, 2, 2, 3, 2, 2, 2, 7, 2, 2, 2, 53, 2, 2, 2, 3, 2, 2, 2, 7, 2, 2, 2, 5, 2, 2, 2, 3, 2, 2, 2, 73, 2, 2, 2, 7, 2, 2, 2, 3, 2, 2, 2, 5

Offset: 2

Author

Colin Barker, Apr 04 2016

Keywords

• nonn

Examples

			a(5) = 5 because A060354(5) = 35 = 5 * 7.
		

Links

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

Crossrefs

Cf. A020639, A060354, A271319, A271320, A271322.

Programs

Mathematica

Table[FactorInteger[PolygonalNumber[n,n]][[1,1]],{n,2,90}] (* Harvey P. Dale, Feb 26 2022 *)

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(n, n))
vector(100, n, n++; a(n))

Formula

a(n) = A020639(A060354(n)).