A055928 Sum of square divisors of n! = sum of squares of divisors of the square root of largest square dividing n!.

1, 1, 1, 5, 5, 210, 210, 850, 7735, 806806, 806806, 3229590, 3229590, 161479500, 1455090000, 23286770000, 23286770000, 838446909300, 838446909300, 83973923013750, 83973923013750, 10244818607677500, 10244818607677500

Offset: 1

Author

Labos Elemer, Jul 21 2000

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..505

Crossrefs

A001157, A000142, A035316, A055772, A000188.

Programs

Mathematica

f[p_, e_] := If[OddQ[e], (p^(e+1)-1)/(p^2-1) , (p^(e+2)-1)/(p^2-1)]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n!]); Array[a, 23] (* Amiram Eldar, Aug 01 2019 *)

Formula

a(n) = A035316(n!) = A001157(A055772(n)) = A001157(A000188(n!)).