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 A002582 M3925 N1613 #51 Sep 08 2022 08:44:31
%S A002582 1,5,23,17,719,5039,1753,2999,125131,7853,479001599,3593203,
%T A002582 87178291199,1510259,6880233439,256443711677,478749547,78143369,
%U A002582 19499250680671,4826713612027,170006681813,498390560021687969,991459181683,114776274341482621993
%N A002582 Largest prime factor of n! - 1.
%D A002582 M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 24-26 (but beware errors).
%D A002582 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002582 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002582 Sean A. Irvine, <a href="/A002582/b002582.txt">Table of n, a(n) for n = 2..135</a>
%H A002582 A. Borning, <a href="http://dx.doi.org/10.1090/S0025-5718-1972-0308018-5 ">Some results for k!+-1 and 2.3.5...p+-1</a>, Math. Comp., 26 (1972), 567-570.
%H A002582 P. Erdős and C. L. Stewart, <a href="http://www.renyi.hu/~p_erdos/1976-27.pdf">On the greatest and least prime factors of n! + 1</a>, J. London Math. Soc. (2) 13:3 (1976), pp. 513-519.
%H A002582 M. Kraitchik, <a href="/A002582/a002582.pdf">On the divisibility of factorials</a>, Scripta Math., 14 (1948), 24-26 (but beware errors). [Annotated scanned copy]
%H A002582 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha105.htm">Factorizations of many number sequences</a>
%H A002582 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha103.htm">Factorizations of many number sequences</a>
%H A002582 R. G. Wilson v, <a href="/A038507/a038507.txt">Explicit factorizations</a>
%H A002582 J. W. Wrench, Jr., <a href="/A002065/a002065_2.pdf">Letters to N. J. A. Sloane, Feb 1974</a>
%F A002582 Erdős & Stewart show that a(n) > n + (l-o(l))log n/log log n and lim sup a(n)/n > 2. - _Charles R Greathouse IV_, Dec 05 2012
%t A002582 Table[FactorInteger[n! - 1][[-1, 1]], {n, 2, 25}] (* _Harvey P. Dale_, Aug 29 2011 *)
%o A002582 (PARI) a(n)=if(n>2,my(f=factor(n!-1)[,1]);f[#f],1) \\ _Charles R Greathouse IV_, Dec 05 2012
%o A002582 (Magma) [1] cat [Maximum(PrimeDivisors(Factorial(n)-1)): n in [3..30]]; // _Vincenzo Librandi_, Feb 14 2020
%Y A002582 Cf. A002583, A033312, A054415, A056110.
%K A002582 nonn,nice
%O A002582 2,2
%A A002582 _N. J. A. Sloane_
%E A002582 More terms from _Robert G. Wilson v_, Aug 01 2000