A056757 Cube of number of divisors is larger than the number.

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

Offset

1,1

Comments

Sequence is finite with 51261 terms. - Charles R Greathouse IV, Apr 27 2011 [Corrected by Amiram Eldar, Jun 02 2024]

The last odd term is a(15199) = 883575. The odd terms are in A056761. - T. D. Noe, May 14 2013

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..51261 (complete sequence, corrected by Amiram Eldar)

Formula

{ k : A000005(k)^3 > k}.

Example

k = 27935107200 = 128*27*25*7*11*13*17*19 has 3072 divisors, 3072^3/k = 1.03779..., so k is a term.

Mathematica

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 *)

Prog

(PARI) is(n)=numdiv(n)^3>n \\ Charles R Greathouse IV, Sep 14 2015

Crossrefs

Cf. A000005, A034884, A035033, A035034, A035035, A056761, A066693.

Cf. A175495 (k < 2^d(k)), A225729-A225738.

Sequence in context: A343185 A070331 A080672 * A349898 A225737 A357315

Adjacent sequences: A056754 A056755 A056756 * A056758 A056759 A056760

Keyword

fini,full,nonn

Author

Labos Elemer, Aug 16 2000

Status

approved