A090630 Greatest divisor d of n! such that d=m^k with k>1.

1, 1, 1, 1, 8, 8, 144, 144, 576, 5184, 518400, 518400, 2073600, 2073600, 101606400, 914457600, 14631321600, 14631321600, 526727577600, 526727577600, 52672757760000, 221225582592000, 6373403688960000, 6373403688960000, 917770131210240000, 22944253280256000000, 3877578804363264000000

Offset

0,5

Comments

a(n) is a square for all n except n = 4, 5 and 21 (Wilke, 1981). - Amiram Eldar, Jun 09 2022

Links

Charles R Greathouse IV, Table of n, a(n) for n = 0..500

Eric Weisstein's World of Mathematics, Perfect Powers.

Eric Weisstein's World of Mathematics, Factorial.

Kenneth M. Wilke, Problem 493, Pi Mu Epsilon Journal, Vol. 7, No. 4 (1981), p. 265; alternative link.

Index entries for sequences related to factorial numbers.

Formula

a(n)= n!/A251753(n). - Robert G. Wilson v, Dec 08 2014

Maple

f:= proc(n)
  local F,  k, d, r, s;
  F:= ifactors(n!)[2];
  r:= 1;
  for k from 2 to F[1][2] do
    r:= max(r, mul(f[1]^(k*floor(f[2]/k)), f=F))
  od:
r
end proc:
1, 1, seq(f(n), n=2..100); # Robert Israel, Dec 08 2014

Mathematica

IsPower[n_] := If[n==1, True, GCD@@(Transpose[FactorInteger[n]][[2]])>1]; Table[Select[Divisors[n! ], IsPower][[ -1]], {n, 0, 25}]

Prog

(PARI) a(n)=my(f=factor(n!), m=1); for(i=2, if(#f~, f[1, 2]), m=max(factorback(concat(Mat(f[, 1]), f[, 2]\i*i)), m)); m \\ Charles R Greathouse IV, Dec 09 2014

Crossrefs

Cf. A011776, A060818, A060828, A251753.

Sequence in context: A065241 A255006 A074191 * A182922 A135808 A320915

Adjacent sequences: A090627 A090628 A090629 * A090631 A090632 A090633

Keyword

nonn

Author

Reinhard Zumkeller, Dec 13 2003

Extensions

More terms from T. D. Noe, Oct 04 2004

Status

approved