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Search: id:A055488
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| A055488 |
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Smallest number x such that sum of divisors of x is n!. |
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+0
3
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| 5, 14, 54, 264, 1560, 10920, 97440, 876960, 10263240, 112895640, 1348827480, 18029171160, 264370186080
(list; graph; listen)
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OFFSET
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3,1
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COMMENT
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for n = 1 a(1) = 1; for n = 2 no solution. Special maximal solutions are the cases when x = n!-1 = prime
a(15) <= 283020617880, a(16) <= 4312201453560, a(17) <= 68995223256960, a(18) <= 1222906341777120 - Vim Wenders (vim(AT)gmx.li), Jan 12 2007
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REFERENCES
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R. K. Guy (1981): Unsolved Problems In Number Theory, B39.
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FORMULA
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a(n) = Min{x; Sigma[x] = n!} = Min{x; A000203(x) = A000142(n)}
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EXAMPLE
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For n = 6 the 15 solutions are as follows: {264,270,280,354,376,406,418,435,459,478,537,623,649,667,719}
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CROSSREFS
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Cf. A000203, A000142.
Sequence in context: A133751 A005504 A073541 this_sequence A127922 A165517 A004030
Adjacent sequences: A055485 A055486 A055487 this_sequence A055489 A055490 A055491
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KEYWORD
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more,nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jun 28 2000
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EXTENSIONS
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More terms from Jud McCranie (j.mccranie(AT)comcast.net), Oct 09 2000
a(13) from Vim Wenders (vim(AT)gmx.li), Nov 06 2006
a(14) from Vim Wenders (vim(AT)gmx.li), Jan 12 2007
a(15) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Aug 26 2008
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