A153825 Sum of proper divisors minus the number of proper divisors of n!.

0, 0, 0, 3, 29, 225, 1669, 14245, 118705, 1118001, 11705019, 144091717, 1738439017, 24817157329, 355309322689, 5378578597729, 86081749391905, 1570394279028289, 28281459220178401, 572031558109560385, 11458497230555053681

Offset

0,4

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Formula

a(n) = A153824(n) - A153823(n) = A152770(A000142(n)).

Maple

with(numtheory): seq(sigma(factorial(n))-factorial(n)-tau(factorial(n))+1, n = 0 .. 22); # Emeric Deutsch, Jan 07 2009

Mathematica

Table[DivisorSigma[1, n!]-n!-(DivisorSigma[0, n!]-1), {n, 0, 20}] (* Harvey P. Dale, Jan 14 2012 *)

Prog

(Magma) [DivisorSigma(1, Factorial(n)) - Factorial(n) - (DivisorSigma(0, Factorial(n))-1): n in [0..20]]; // Vincenzo Librandi, Aug 31 2016
(PARI) a(n) = (sigma(n!) - n!) - (numdiv(n!) - 1); \\ Michel Marcus, Aug 31 2016

Crossrefs

Cf. A000005, A000142, A000203, A001065, A032741, A062569, A152770, A153823, A153824.

Sequence in context: A083092 A174419 A220548 * A201490 A354402 A135163

Adjacent sequences: A153822 A153823 A153824 * A153826 A153827 A153828

Keyword

nonn

Author

Omar E. Pol, Jan 02 2009

Extensions

Extended by Emeric Deutsch, Jan 07 2009

Status

approved