A260234 Largest prime factor of the n-th hexagonal number (A000384).

3, 5, 7, 5, 11, 13, 5, 17, 19, 11, 23, 13, 7, 29, 31, 17, 7, 37, 13, 41, 43, 23, 47, 7, 17, 53, 11, 29, 59, 61, 7, 13, 67, 23, 71, 73, 19, 13, 79, 41, 83, 43, 29, 89, 23, 47, 19, 97, 11, 101, 103, 53, 107, 109, 37, 113, 29, 59, 17, 61, 41, 7, 127, 43, 131

Offset: 2

Author

Colin Barker, Jul 20 2015

Keywords

• nonn

Comments

As A000384(n+1) = (n*2+1)*(n*1+1), A000384(n) belongs to A180045 for n > 3, and a(n) tends to infinity as n tends to infinity. - Rémy Sigrist, Feb 23 2020

Examples

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

Links

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

Crossrefs

Cf. A000384, A006530, A180045, A260233, A260235, A260236.

Programs

Mathematica

FactorInteger[#][[-1,1]]&/@PolygonalNumber[6,Range[2,70]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 10 2018 *)

PARI

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

Formula

a(n) = A006530(A000384(n)).