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A064138
Sum of non-unitary divisors of n!.
1
0, 0, 0, 24, 144, 1398, 11184, 97200, 973296, 10950696, 131408352, 1593191808, 22304685312, 333297226080, 5103130001760, 81686161277280, 1470350902991040, 26490792085668288, 529815841713365760, 10635027891469974720
OFFSET
1,4
LINKS
FORMULA
a(n) = sigma(n!) - usigma(n!) = A000203(n!) - A034448(A000142(n)) = A062569(n) - A034448(n!) = A048105(n!).
EXAMPLE
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.
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 *)
PROG
(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
KEYWORD
nonn
AUTHOR
Labos Elemer, Sep 11 2001
EXTENSIONS
Term corrected and more terms added by Harry J. Smith, Sep 08 2009
STATUS
approved