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%I #9 Aug 31 2022 19:42:38
%S 2,5,7,173,563,73,41,369581,1409,109,449,176459,44221,12148537,148381,
%T 11399977,5779337237,151431487,26013917,57405011,939783003793,277157,
%U 191141,13515438731,79702499,236463558839,1883371283883863,313527009031,138961158000728258971
%N a(n) = largest prime in the factorization of n-th Franel number (A000172).
%H Sean A. Irvine, <a href="/A058854/b058854.txt">Table of n, a(n) for n = 1..150</a>
%e a(4)=173 because the 4th Franel number is 346 = 2^1 * 173^1, in which 173 is the largest prime.
%p with(combinat): with(numtheory): A000172 := n->sum(binomial(n,k)^3, k=0..n): for n from 1 to 50 do printf(`%d,`, sort(ifactors(A000172(n))[2])[nops(ifactors(A000172(n))[2])][1]) od: # Corrected by _Sean A. Irvine_, Aug 31 2022
%p # second Maple program:
%p a:= n-> max(numtheory[factorset](add(binomial(n, k)^3, k=0..n))):
%p seq(a(n), n=1..30); # _Alois P. Heinz_, Aug 31 2022
%t Do[ Print[ FactorInteger[ Sum[ Binomial[n, k]^3, {k, 0, n}]] [[ -1, 1]] ], {n, 1, 32} ]
%Y Cf. A000172.
%K nonn
%O 1,1
%A Felix Goldberg (felixg(AT)tx.technion.ac.il), Jan 30 2001
%E More terms from _James A. Sellers_, Feb 01 2001
%E Data corrected and entry revised by _Sean A. Irvine_, Aug 31 2022
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