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(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
KEYWORD
easy,nonn
AUTHOR
Jason Earls, Jul 03 2001
STATUS
approved