cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A056762 Number of terms in A056761 (i.e., odd numbers from A056757) between 2^(n-1) and 2^n.

Original entry on oeis.org

0, 1, 2, 2, 3, 8, 5, 12, 19, 13, 25, 31, 22, 33, 28, 17, 24, 12, 6, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Labos Elemer, Aug 16 2000

Keywords

Comments

A056761 is finite and has 267 terms.

Examples

			The last 4 terms arise between 524288 and 1048576: {675675, 765765, 855855, 883575}, thus here a(20)=4. For n > 20, a(n)=0.

Crossrefs

Cf. A000005, A029837, A035033-A035035, A034884, A056757-A056767.

Formula

Occurrences of odd integers x such that 2^(n-1) < x <= 2^n and the cube of number of divisors is larger than the number: A000005(x)^3 > x.

Extensions

More terms from Sean A. Irvine, May 05 2022

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

Original entry on oeis.org

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

Views

Author

Labos Elemer, Aug 16 2000

Keywords

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

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}.
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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