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A061556 Least k such that sigma(k!)>=n*k!. 0
1, 3, 5, 9, 14, 23, 43, 79, 149, 263, 461, 823, 1451, 2549, 4483, 7879, 13859, 24247, 42683, 75037 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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.

LINKS

Table of n, a(n) for n=0..19.

Achim Flammenkamp, The Multiply Perfect Numbers Page

Fred Helenius, Link to Glossary and Lists

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.

Sequence in context: A120452 A144116 A294424 * A053993 A071155 A120695

Adjacent sequences:  A061553 A061554 A061555 * A061557 A061558 A061559

KEYWORD

nonn

AUTHOR

Labos Elemer, May 17 2001

EXTENSIONS

More terms from David Wasserman, Jun 18 2002

STATUS

approved

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Last modified February 21 04:18 EST 2019. Contains 320371 sequences. (Running on oeis4.)