A073081 Greatest k such that k! divides sigma(n!).

1, 1, 3, 3, 5, 3, 4, 6, 6, 2, 4, 4, 4, 7, 7, 7, 7, 4, 9, 7, 8, 8, 11, 8, 8, 10, 10, 9, 10, 13, 14, 13, 6, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 8, 11, 11, 12, 19, 21, 16, 16, 16, 14, 14, 12, 16, 16, 16, 16, 16, 16, 22, 21, 21, 21, 19, 19, 20, 20, 20, 20, 22, 21, 21, 19, 14

Offset: 1

Author

Benoit Cloitre, Aug 17 2002

Keywords

• easy
• nonn

Comments

sum(k=1,n,a(k)) seems to be asymptotic to C*n^2 with 1/20 < C < 1/10.

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A062569 (sigma(n!)).

Programs

PARI

a(n) = my(m=1, s=sigma(n!)); for (k=1, n, if ((s % k!) == 0, m = max(m, k))); m; \\ Michel Marcus, Dec 05 2019