A064138 Sum of non-unitary divisors of n!.

0, 0, 0, 24, 144, 1398, 11184, 97200, 973296, 10950696, 131408352, 1593191808, 22304685312, 333297226080, 5103130001760, 81686161277280, 1470350902991040, 26490792085668288, 529815841713365760, 10635027891469974720

Offset: 1

Author

Labos Elemer, Sep 11 2001

Keywords

• nonn

Examples

			For n = 6, 6! = 720, the sum of its 30 divisors is 2418, the sum of the 8 unitary divisors is 1020, so the remaining 22 divisors give a(6) = 1398.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A034448, A048105, A046656, A056657, A056171, A056172, A000203, A000142, A062569, A063955, A063960.

Programs

Mathematica

f1[p_, e_] := (p^(e + 1) - 1)/(p - 1); f2[p_, e_] := p^e + 1; a[n_] := Times @@ f1 @@@ (fct = FactorInteger[n!]) - Times @@ f2 @@@ fct; a[1] = 0; Array[a, 20] (* Amiram Eldar, Apr 01 2024 *)

PARI

usigma(n)= { local(f,s=1); f=factor(n); for(i=1, matsize(f)[1], s*=1 + f[i, 1]^f[i, 2]); return(s) }
{ n=0; f=1; for (n=1, 100, f*=n; write("b064138.txt", n, " ", sigma(f) - usigma(f)); ) } \\ Harry J. Smith, Sep 08 2009

Formula

a(n) = sigma(n!) - usigma(n!) = A000203(n!) - A034448(A000142(n)) = A062569(n) - A034448(n!) = A048105(n!).

Extensions

Term corrected and more terms added by Harry J. Smith, Sep 08 2009