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 A002582 Largest prime factor of n! - 1. (Formerly M3925 N1613) 6

%I M3925 N1613

%S 1,5,23,17,719,5039,1753,2999,125131,7853,479001599,3593203,

%T 87178291199,1510259,6880233439,256443711677,478749547,78143369,

%U 19499250680671,4826713612027,170006681813,498390560021687969

%N Largest prime factor of n! - 1.

%D A. Borning, Some results for k!+-1 and 2.3.5...p+-1, Math. Comp., 26 (1972), 567-570.

%D M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 24-26 (but beware errors).

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H 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 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha105.htm">Factorizations of many number sequences</a>

%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha103.htm">Factorizations of many number sequences</a>

%H R. G. Wilson v, <a href="/A038507/a038507.txt">Explicit factorizations</a>

%F 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 Table[FactorInteger[n!-1][[-1,1]],{n,2,25}] (* From Harvey P. Dale, Aug 29 2011 *)

%o (PARI) a(n)=if(n>2,my(f=factor(n!-1)[,1]);f[#f],1) \\ _Charles R Greathouse IV_, Dec 05 2012

%Y Cf. A002583, A033312, A054415, A056110.

%K nonn,nice

%O 2,2

%A _N. J. A. Sloane_.

%E More terms from _Robert G. Wilson v_, Aug 01 2000

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Last modified May 23 14:09 EDT 2013. Contains 225595 sequences.