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A061556
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Least k such that sigma(k!)>=n*k!.
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0
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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; internal format)
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OFFSET
| 0,2
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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 (benoit7848c(AT)orange.fr), 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.
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LINKS
| Achim Flammenkamp, The Multiply Perfect Numbers Page
Fred Helenius, Link to Glossary and Lists
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FORMULA
| a(n)=Min{w | Floor[Sigma(w!)/w!=n]
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EXAMPLE
| Floor[ sigma(842!)/842! ]=11 while Floor[ sigma(843!)/843! ]=12
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PROG
| (PARI) a(n)=if(n<0, 0, s=1; while(sigma(s!)<n*s!, s++); s)
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CROSSREFS
| Cf. A000142, A000203, A023199.
Sequence in context: A033818 A120452 A144116 * A053993 A071155 A120695
Adjacent sequences: A061553 A061554 A061555 * A061557 A061558 A061559
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), May 17 2001
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EXTENSIONS
| More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Jun 18 2002
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