A061556 a(n) is the least k > 0 such that sigma(k!) >= n*k!.

1, 1, 3, 5, 9, 14, 23, 43, 79, 149, 263, 461, 823, 1451, 2549, 4483, 7879, 13859, 24247, 42683, 75037, 131707, 230773, 405401, 710569, 1246379, 2185021, 3831913, 6720059, 11781551, 20657677

Offset

0,3

Comments

It seems that, for n > 1, a(n+1) < 2*a(n). Does lim_{n -> infinity} a(n+1)/a(n) = 2? - Benoit Cloitre, Aug 18 2002

Smallest number m such that the abundancy-index of m! is at least n.

Floor(sigma(m!)/m!) = n; note that abundancy-index [= sigma(u)/u] here is not necessarily an integer.

It appears that a(n) = A091440(n) for n >= 13. - Daniel Suteu, Sep 03 2019

Links

Table of n, a(n) for n=0..30.

Achim Flammenkamp, The Multiply Perfect Numbers Page.

Fred Helenius, Multiperfect numbers.

Formula

a(n) = Min{w | floor(sigma(w!)/w!) = n}.

Example

floor(sigma(842!)/842!) = 11 while floor(sigma(843!)/843!) = 12.

Prog

(PARI) a(n)=if(n<0, 0, s=1; while(sigma(s!)<n*s!, s++); s)

Crossrefs

Cf. A000142, A000203, A023199, A062569.

Sequence in context: A120452 A144116 A294424 * A053993 A327562 A071155

Adjacent sequences: A061553 A061554 A061555 * A061557 A061558 A061559

Keyword

nonn,more

Author

Labos Elemer, May 17 2001

Extensions

More terms from David Wasserman, Jun 18 2002

a(1) inserted and a(21)-a(30) added by Daniel Suteu, Sep 03 2019

Status

approved