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 A083397 #17 Apr 13 2024 15:02:11
%S A083397 0,2,3,5,11,3,71,67,67,127,13,509,137,37,71471,71471,409993,941351,
%T A083397 24419,287093,7147792819,110647261,80392811773,4716679469,4716679469,
%U A083397 323905128133,8392290961,551615338229,34178276390953,73669621631
%N A083397 Largest prime factor of n! + k where k is the least positive integer such that n! + k is a square.
%C A083397 For n > 1, n! cannot be a perfect square. Proof: All exponents of the prime factors of a square are even. But in the factorization of n! at least one of the primes will appear only once due to Bertrand's Postulate which says there is always a prime between m and 2m.
%H A083397 Amiram Eldar, <a href="/A083397/b083397.txt">Table of n, a(n) for n = 1..100</a>
%e A083397 a(9)=67 because 9!+729 = 363609 = 3^4*67^2 is a square with largest prime factor of 67.
%t A083397 Join[{0},Table[FactorInteger[(Floor[Sqrt[n!]]+1)^2][[-1,1]],{n,2,30}]] (* _Harvey P. Dale_, Jan 04 2012 *)
%Y A083397 Cf. A068869.
%K A083397 nonn
%O A083397 1,2
%A A083397 _Jason Earls_, Jun 06 2003