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

Author

Labos Elemer, Aug 16 2000

Keywords

• fini
• full
• nonn

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

Examples

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

Links

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

Crossrefs

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

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

Programs

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 *)

PARI

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

Formula

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