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

1, 5, 23, 17, 719, 5039, 1753, 2999, 125131, 7853, 479001599, 3593203, 87178291199, 1510259, 6880233439, 256443711677, 478749547, 78143369, 19499250680671, 4826713612027, 170006681813, 498390560021687969, 991459181683, 114776274341482621993

Offset

2,2

References

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).

Links

Sean A. Irvine, Table of n, a(n) for n = 2..135

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

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.

M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 24-26 (but beware errors). [Annotated scanned copy]

Hisanori Mishima, Factorizations of many number sequences

Hisanori Mishima, Factorizations of many number sequences

R. G. Wilson v, Explicit factorizations

J. W. Wrench, Jr., Letters to N. J. A. Sloane, Feb 1974

Formula

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

Mathematica

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

Prog

(PARI) a(n)=if(n>2, my(f=factor(n!-1)[, 1]); f[#f], 1) \\ Charles R Greathouse IV, Dec 05 2012
(Magma) [1] cat [Maximum(PrimeDivisors(Factorial(n)-1)): n in [3..30]]; // Vincenzo Librandi, Feb 14 2020

Crossrefs

Cf. A002583, A033312, A054415, A056110.

Sequence in context: A081319 A177242 A233756 * A368425 A102723 A136146

Adjacent sequences: A002579 A002580 A002581 * A002583 A002584 A002585

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

More terms from Robert G. Wilson v, Aug 01 2000

Status

approved