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Search: id:A061556
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| A061556 |
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Least k such that sigma(k!)>=n*k!. |
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+0
1
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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; listen)
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OFFSET
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0,2
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COMMENT
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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
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Achim Flammenkamp, The Multiply Perfect Numbers Page
Fred Helenius, Link to Glossary and Lists
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FORMULA
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a(n)=Min{w | Floor[Sigma(w!)/w!=n]
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EXAMPLE
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Floor[ sigma(842!)/842! ]=11 while Floor[ sigma(843!)/843! ]=12
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PROGRAM
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(PARI) a(n)=if(n<0, 0, s=1; while(sigma(s!)<n*s!, s++); s)
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CROSSREFS
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Cf. A000142, A000203, A023199.
Adjacent sequences: A061553 A061554 A061555 this_sequence A061557 A061558 A061559
Sequence in context: A032801 A033818 A120452 this_sequence A053993 A071155 A120695
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), May 17 2001
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Jun 18 2002
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