

A056757


Cube of number of divisors is larger than the number.


20



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

1,1


COMMENTS

Sequence is finite with 50967 elements.  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


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..50967 (complete sequence)


FORMULA

d(n)^3 > n, where d=A000005.


EXAMPLE

n = 27935107200 = 128*27*25*7*11*13*17*19 has 3072 divisors, its cube 28991029248/n = 1.037799, so n is here.


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. A034884, A035033A035035.
Cf. A175495 (n < 2^d(n)), A225729A225738.
Sequence in context: A164713 A070331 A080672 * A225737 A079333 A063938
Adjacent sequences: A056754 A056755 A056756 * A056758 A056759 A056760


KEYWORD

fini,full,nonn


AUTHOR

Labos Elemer, Aug 16 2000


STATUS

approved



