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A056757
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Cube of number of divisors is larger than the number.
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20
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2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 66, 68, 70, 72, 75, 76, 78, 80, 81, 84, 88, 90, 92, 96, 98, 99, 100, 102, 104, 105, 108, 110
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OFFSET
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1,1
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COMMENTS
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Sequence is finite with 50967 terms. - Charles R Greathouse IV, Apr 27 2011
The last odd term is a(15199) = 883575. The odd terms are in A056761. - T. D. Noe, May 14 2013
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n = 1..50967 (complete sequence)
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FORMULA
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{ k : A000005(k)^3 > k}.
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EXAMPLE
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k = 27935107200 = 128*27*25*7*11*13*17*19 has 3072 divisors, 3072^3/k = 1.03779..., so k is a term.
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MATHEMATICA
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t = {}; Do[If[n < DivisorSigma[0, n]^3, AppendTo[t, n]], {n, 10^3}]; t (* T. D. Noe, May 14 2013 *)
Select[Range[120], DivisorSigma[0, #]^3>#&] (* Harvey P. Dale, Apr 22 2019 *)
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PROG
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(PARI) is(n)=numdiv(n)^3>n \\ Charles R Greathouse IV, Sep 14 2015
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CROSSREFS
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Cf. A034884, A035033-A035035.
Cf. A175495 (n < 2^d(n)), A225729-A225738.
Sequence in context: A343185 A070331 A080672 * A349898 A225737 A357315
Adjacent sequences: A056754 A056755 A056756 * A056758 A056759 A056760
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KEYWORD
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fini,full,nonn
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AUTHOR
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Labos Elemer, Aug 16 2000
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STATUS
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approved
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