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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 (list; graph; refs; listen; history; text; internal format)
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 *)

PROG

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

CROSSREFS

Cf. A034884, A035033-A035035.

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

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

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Last modified August 19 01:46 EDT 2017. Contains 290790 sequences.