A056110 Highest proper factor of n!-1, or a(n)=1 if n!-1 is not composite.

1, 1, 1, 17, 1, 1, 1753, 32989, 125131, 3070523, 1, 3593203, 1, 76922021647, 6880233439, 18720390952421, 108514808571661, 186286524362683, 19499250680671, 2221345311813453913, 10311933282363373211, 498390560021687969, 991459181683, 104102080827724738147651, 19739193437746837432529

Offset: 2

Author

Henry Bottomley, Jun 12 2000

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 2..135
• Hisanori Mishima, Factorizations of many number sequences: n! - 1 (n = 1 to 100).
• R. G. Wilson v, Explicit factorizations

Crossrefs

Cf. A002582.

Programs

Mathematica

pf[n_]:=Module[{c=n!-1},If[PrimeQ[c],1,c/FactorInteger[c][[1,1]]]]; Array[pf,30,2] (* Harvey P. Dale, Dec 13 2012 *)

PARI

A056110(n)={n=factor(n!-1);if(norml2(n[,2])>1,factorback(n)/n[1,1],1)} \\ M. F. Hasler, Oct 31 2012

Formula

a(n) = A033312(n)/A054415(n)

Extensions

Edited and extended by M. F. Hasler, Oct 31 2012