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A002582
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Largest prime factor of n! - 1.
(Formerly M3925 N1613)
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6
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1, 5, 23, 17, 719, 5039, 1753, 2999, 125131, 7853, 479001599, 3593203, 87178291199, 1510259, 6880233439, 256443711677, 478749547, 78143369, 19499250680671, 4826713612027, 170006681813, 498390560021687969
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OFFSET
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2,2
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REFERENCES
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A. Borning, Some results for k!+-1 and 2.3.5...p+-1, Math. Comp., 26 (1972), 567-570.
M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 24-26 (but beware errors).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=2..23.
P. Erdős and C. L. Stewart, On the greatest and least prime factors of n! + 1, J. London Math. Soc. (2) 13:3 (1976), pp. 513-519.
Hisanori Mishima, Factorizations of many number sequences
Hisanori Mishima, Factorizations of many number sequences
R. G. Wilson v, Explicit factorizations
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FORMULA
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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
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MATHEMATICA
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Table[FactorInteger[n!-1][[-1, 1]], {n, 2, 25}] (* From Harvey P. Dale, Aug 29 2011 *)
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PROG
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(PARI) a(n)=if(n>2, my(f=factor(n!-1)[, 1]); f[#f], 1) \\ Charles R Greathouse IV, Dec 05 2012
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CROSSREFS
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Cf. A002583, A033312, A054415, A056110.
Sequence in context: A078190 A081319 A177242 * A102723 A136146 A167804
Adjacent sequences: A002579 A002580 A002581 * A002583 A002584 A002585
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Robert G. Wilson v, Aug 01 2000
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STATUS
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approved
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