A062569 a(n) = sigma(n!).

1, 1, 3, 12, 60, 360, 2418, 19344, 159120, 1481040, 15334088, 184009056, 2217441408, 31044179712, 442487616480, 6686252969760, 107004539285280, 1926081707135040, 34683832925921088, 693676658518421760, 13891399238731734720, 292460416142501376000

Offset

0,3

References

Wacław Sierpiński, Elementary Theory of Numbers, Ex. 6, p. 169, Warsaw, 1964.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..300

Rafael Jakimczuk, Two topics in number theory: sum of divisors of the factorial and a formula for primes, International Mathematical Forum, Vol. 12, No. 19 (2017), pp. 929-935. See Theorem 1.4, p. 932.

Vaclav Kotesovec, Plot of a(n)/(n!*log(n)) for n = 2..50000.

Formula

a(n) = A000203(A000142(n)). - Michel Marcus, Jan 10 2015

a(p) = (p+1)*a(p-1) for p prime. - Altug Alkan, Jul 18 2016

Limit_{n->oo} a(n)/n! = oo. Proof in Sierpiński. - Bernard Schott, Feb 09 2019

a(n) ~ c * n! * log(n) * (1 + O(1/log(n))), where c = exp(gamma) = A073004 (Jakimczuk, 2017). - Amiram Eldar, Nov 07 2020

Example

a(4) = 60, since the sum of the positive divisors of 4! is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60. - Timothy L. Tiffin, Jan 22 2023

Maple

with(numtheory):seq(sigma(n!), n=0..19); # Zerinvary Lajos, Feb 15 2008

Mathematica

Array[DivisorSigma[1, #! ]&, 33, 1] (* Vladimir Joseph Stephan Orlovsky, Nov 01 2009 *)

Prog

(PARI) for(n=0, 21, print(sigma(n!)))
(Sage) [sigma(ZZ(n).factorial(), 1) for n in range(20)]  # Zerinvary Lajos, Jun 13 2009

Crossrefs

Cf. A000142, A000203, A027423, A073004.

Sequence in context: A326242 A070863 A180707 * A089057 A077134 A001710

Adjacent sequences: A062566 A062567 A062568 * A062570 A062571 A062572

Keyword

easy,nonn

Author

Jason Earls, Jul 03 2001

Status

approved