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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
2
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| 5, 14, 54, 264, 1560, 10920, 97440, 876960, 10263240, 112895640, 1348827480, 18029171160
(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 A004030 A128102
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
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