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

%I A260233 #8 May 05 2016 10:34:34
%S A260233 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 A260233 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 A260233 2,3,2,3,2,5,2,3,2,3,2,79,2,3,2,3,2,5,2
%N A260233 Smallest prime factor of the n-th hexagonal number (A000384).
%H A260233 Colin Barker, <a href="/A260233/b260233.txt">Table of n, a(n) for n = 2..1000</a>
%F A260233 a(n) = A020639(A000384(n)).
%e A260233 a(3) = 3 because A000384(3) = 15 = 3 * 5.
%t A260233 Table[FactorInteger[n(2n-1)][[1,1]],{n,2,100}] (* _Harvey P. Dale_, May 05 2016 *)
%o A260233 (PARI)
%o A260233 pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
%o A260233 spf(m) = factorint(m)[1,1] \\ Smallest prime factor
%o A260233 a(n) = spf(pg(6, n))
%Y A260233 Cf. A000384, A020639, A260234, A260235, A260236.
%K A260233 nonn
%O A260233 2,1
%A A260233 _Colin Barker_, Jul 20 2015