This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A058854 #10 Jul 02 2025 16:02:00
%S A058854 2,5,7,173,563,73,41,369581,1409,109,449,176459,44221,12148537,148381,
%T A058854 11399977,5779337237,151431487,26013917,57405011,939783003793,277157,
%U A058854 191141,13515438731,79702499,236463558839,1883371283883863,313527009031,138961158000728258971
%N A058854 a(n) = largest prime in the factorization of n-th Franel number (A000172).
%H A058854 Sean A. Irvine, <a href="/A058854/b058854.txt">Table of n, a(n) for n = 1..150</a>
%e A058854 a(4)=173 because the 4th Franel number is 346 = 2^1 * 173^1, in which 173 is the largest prime.
%p A058854 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 A058854 # second Maple program:
%p A058854 a:= n-> max(numtheory[factorset](add(binomial(n, k)^3, k=0..n))):
%p A058854 seq(a(n), n=1..30); # _Alois P. Heinz_, Aug 31 2022
%t A058854 Do[ Print[ FactorInteger[ Sum[ Binomial[n, k]^3, {k, 0, n}]] [[ -1, 1]] ], {n, 1, 32} ]
%Y A058854 Cf. A000172.
%K A058854 nonn
%O A058854 1,1
%A A058854 Felix Goldberg (felixg(AT)tx.technion.ac.il), Jan 30 2001
%E A058854 More terms from _James Sellers_, Feb 01 2001
%E A058854 Data corrected and entry revised by _Sean A. Irvine_, Aug 31 2022