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Largest prime factor of the n-th hexagonal number (A000384).
6

%I #11 Feb 23 2020 07:08:29

%S 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,

%T 53,11,29,59,61,7,13,67,23,71,73,19,13,79,41,83,43,29,89,23,47,19,97,

%U 11,101,103,53,107,109,37,113,29,59,17,61,41,7,127,43,131

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

%C 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

%H Colin Barker, <a href="/A260234/b260234.txt">Table of n, a(n) for n = 2..1000</a>

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

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

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

%o (PARI)

%o pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number

%o lpf(m) = vecmax(factorint(m)[, 1]) \\ Largest prime factor

%o a(n) = lpf(pg(6, n))

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

%K nonn

%O 2,1

%A _Colin Barker_, Jul 20 2015