A056110 - OEIS

%I #16 Oct 07 2019 11:15:21

%S 1,1,1,17,1,1,1753,32989,125131,3070523,1,3593203,1,76922021647,

%T 6880233439,18720390952421,108514808571661,186286524362683,

%U 19499250680671,2221345311813453913,10311933282363373211,498390560021687969,991459181683,104102080827724738147651,19739193437746837432529

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

%H Amiram Eldar, <a href="/A056110/b056110.txt">Table of n, a(n) for n = 2..135</a>

%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha105.htm">Factorizations of many number sequences: n! - 1 (n = 1 to 100)</a>.

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

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

%t 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 *)

%o (PARI) A056110(n)={n=factor(n!-1);if(norml2(n[,2])>1,factorback(n)/n[1,1],1)} \\ _M. F. Hasler_, Oct 31 2012

%Y Cf. A002582.

%K nonn

%O 2,4

%A _Henry Bottomley_, Jun 12 2000

%E Edited and extended by _M. F. Hasler_, Oct 31 2012