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Sum of proper divisors of n!: a(n) = sigma(n!) - n!.
2

%I #14 Sep 08 2022 08:45:40

%S 0,0,1,6,36,240,1698,14304,118800,1118160,11705288,144092256,

%T 1738439808,24817158912,355309325280,5378578601760,86081749397280,

%U 1570394279039040,28281459220193088,572031558109589760,11458497230555094720

%N Sum of proper divisors of n!: a(n) = sigma(n!) - n!.

%C a(n) is the sum of proper divisors of factorial number A000142(n).

%H G. C. Greubel, <a href="/A153824/b153824.txt">Table of n, a(n) for n = 0..500</a>

%F a(n) = A000203(n!) - n! = A062569(n) - A000142(n) = A001065(A000142(n)).

%p with(numtheory): seq(sigma(factorial(n))-factorial(n), n = 0 .. 22); # _Emeric Deutsch_, Jan 07 2009

%t Table[DivisorSigma[1, n!] - n!, {n, 0, 50}] (* _G. C. Greubel_, Aug 30 2016 *)

%o (Magma) [DivisorSigma(1,Factorial(n)) - Factorial(n): n in [0..20]]; // _Vincenzo Librandi_, Aug 31 2016

%o (PARI) a(n) = sigma(n!) - n!; \\ _Michel Marcus_, Aug 31 2016

%Y Cf. A000142, A000203, A001065, A062569.

%K nonn

%O 0,4

%A _Omar E. Pol_, Jan 02 2009

%E Extended by _Emeric Deutsch_, Jan 07 2009