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.

Showing 1-10 of 11 results. Next

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}.

A225738 Number of numbers k such that k < d(k)^(n/10), where d(k) is the number of divisors of k.

Original entry on oeis.org

0, 1, 1, 3, 4, 4, 7, 14, 21, 29, 52, 89, 155, 284, 528, 1018, 2046, 4282, 9272, 21466, 50967
Offset: 10

Views

Author

T. D. Noe, May 14 2013

Keywords

Crossrefs

Cf. A034884 (n < d(n)^2), A056757 (n < d(n)^3), A225729-A225737.

Programs

  • Mathematica
    Table[f = 0; Do[If[k < DivisorSigma[0, k]^(n/10), f++], {k, 10^4}]; f, {n, 10, 20}]

A225730 Numbers k such that k < d(k)^(22/10), where d(k) is the number of divisors of k.

Original entry on oeis.org

2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 54, 56, 60, 64, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 108, 112, 120, 126, 132, 140, 144, 150, 156, 160, 168, 180, 192, 198, 200, 204, 210, 216, 220, 224, 228, 234
Offset: 1

Views

Author

T. D. Noe, May 14 2013

Keywords

Comments

Alternatively, we could write k^5 < d(k)^11. The last odd number is a(23) = 45.

Links

Crossrefs

Cf. A000005, A034884 (k < d(k)^2), A175495 (k < 2^d(k)), A056757 (k < d(k)^3).
Cf. A225729-A225738, A353448.

Programs

  • Mathematica
    t = {}; Do[If[n < DivisorSigma[0, n]^(22/10), AppendTo[t, n]], {n, 10^5}]; t
Select[Range[250],#Harvey P. Dale, Apr 10 2024 *)
  • PARI
    for (k=2, 20000, if (k^5 < numdiv(k)^11, print1(k,", "))) \\ Hugo Pfoertner, Apr 25 2023

A225737 Numbers n such that n < d(n)^(29/10), where d(n) is the number of divisors of n.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 60, 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

T. D. Noe, May 14 2013

Keywords

Comments

Alternatively, we could write n^10 < d(n)^29. The last odd term is a(6362) = 225225.

Links

Crossrefs

Cf. A034884 (n < d(n)^2), A175495 (n < 2^d(n)), A056757 (n < d(n)^3).
Cf. A225729-A225738.

Programs

  • Mathematica
    t = {}; Do[If[n < DivisorSigma[0, n]^(29/10), AppendTo[t, n]], {n, 10^7}]; t

A225731 Numbers n such that n < d(n)^(23/10), where d(n) is the number of divisors of n.

Original entry on oeis.org

2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 64, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 105, 108, 110, 112, 114, 120, 126, 132, 140, 144, 150, 156, 160, 162, 168, 176, 180, 192
Offset: 1

Views

Author

T. D. Noe, May 14 2013

Keywords

Comments

Alternatively, we could write n^10 < d(n)^23. The last odd number is a(44) = 105.

Links

Crossrefs

Cf. A034884 (n < d(n)^2), A175495 (n < 2^d(n)), A056757 (n < d(n)^3).
Cf. A225729-A225738.

Programs

  • Mathematica
    t = {}; Do[If[n < DivisorSigma[0, n]^(23/10), AppendTo[t, n]], {n, 10^5}]; t

A225732 Numbers n such that n < d(n)^(24/10), where d(n) is the number of divisors of n.

Original entry on oeis.org

2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 63, 64, 66, 68, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 105, 108, 110, 112, 114, 120, 126, 128, 130, 132, 135, 136, 138, 140
Offset: 1

Views

Author

T. D. Noe, May 14 2013

Keywords

Comments

Alternatively, we could write n^5 < d(n)^12. The last odd number is a(95) = 315.

Links

Crossrefs

Cf. A034884 (n < d(n)^2), A175495 (n < 2^d(n)), A056757 (n < d(n)^3).
Cf. A225729-A225738.

Programs

  • Mathematica
    t = {}; Do[If[n < DivisorSigma[0, n]^(24/10), AppendTo[t, n]], {n, 10^6}]; t

A225733 Numbers n such that n < d(n)^(5/2), where d(n) is the number of divisors of n.

Original entry on oeis.org

2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 63, 64, 66, 68, 70, 72, 75, 76, 78, 80, 84, 88, 90, 96, 100, 102, 104, 105, 108, 110, 112, 114, 120, 126, 128, 130, 132, 135, 136, 138
Offset: 1

Views

Author

T. D. Noe, May 14 2013

Keywords

Comments

Alternatively, we could write n^2 < d(n)^5. The last odd number is a(206) = 945.

Links

Crossrefs

Cf. A034884 (n < d(n)^2), A175495 (n < 2^d(n)), A056757 (n < d(n)^3).
Cf. A225729-A225738.

Programs

  • Mathematica
    t = {}; Do[If[n < DivisorSigma[0, n]^(5/2), AppendTo[t, n]], {n, 10^6}]; t

A225734 Numbers n such that n < d(n)^(26/10), where d(n) is the number of divisors of n.

Original entry on oeis.org

2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 63, 64, 66, 68, 70, 72, 75, 76, 78, 80, 84, 88, 90, 92, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 120, 126, 128
Offset: 1

Views

Author

T. D. Noe, May 14 2013

Keywords

Comments

Alternatively, we could write n^5 < d(n)^13. The last odd number is a(473) = 3465.

Links

Crossrefs

Cf. A034884 (n < d(n)^2), A175495 (n < 2^d(n)), A056757 (n < d(n)^3).
Cf. A225729-A225738.

Programs

  • Mathematica
    t = {}; Do[If[n < DivisorSigma[0, n]^(26/10), AppendTo[t, n]], {n, 10^7}]; t

A225735 Numbers n such that n < d(n)^(27/10), where d(n) is the number of divisors of n.

Original entry on oeis.org

2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 63, 64, 66, 68, 70, 72, 75, 76, 78, 80, 84, 88, 90, 92, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 116
Offset: 1

Views

Author

T. D. Noe, May 14 2013

Keywords

Comments

Alternatively, we could write n^10 < d(n)^27. The last odd term is a(995) = 10395.

Links

Crossrefs

Cf. A034884 (n < d(n)^2), A175495 (n < 2^d(n)), A056757 (n < d(n)^3).
Cf. A225729-A225738.

Programs

  • Mathematica
    t = {}; Do[If[n < DivisorSigma[0, n]^(27/10), AppendTo[t, n]], {n, 10^7}]; t

A225736 Numbers n such that n < d(n)^(28/10), where d(n) is the number of divisors of n.

Original entry on oeis.org

2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 52, 54, 56, 60, 63, 64, 66, 68, 70, 72, 75, 76, 78, 80, 81, 84, 88, 90, 92, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114
Offset: 1

Views

Author

T. D. Noe, May 14 2013

Keywords

Comments

Alternatively, we could write n^5 < d(n)^14. The last odd term is a(2447) = 45045.

Links

Crossrefs

Cf. A034884 (n < d(n)^2), A175495 (n < 2^d(n)), A056757 (n < d(n)^3).
Cf. A225729-A225738.

Programs

  • Mathematica
    t = {}; Do[If[n < DivisorSigma[0, n]^(28/10), AppendTo[t, n]], {n, 10^7}]; t
Showing 1-10 of 11 results. Next

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

Content is available under The OEIS End-User License Agreement.