login
Sum of square divisors of n! = sum of squares of divisors of the square root of largest square dividing n!.
1

%I #10 Aug 01 2019 11:31:42

%S 1,1,1,5,5,210,210,850,7735,806806,806806,3229590,3229590,161479500,

%T 1455090000,23286770000,23286770000,838446909300,838446909300,

%U 83973923013750,83973923013750,10244818607677500,10244818607677500

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

%H Amiram Eldar, <a href="/A055928/b055928.txt">Table of n, a(n) for n = 1..505</a>

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

%t 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 *)

%Y A001157, A000142, A035316, A055772, A000188.

%K nonn

%O 1,4

%A _Labos Elemer_, Jul 21 2000