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 1-3 of 3 results.

A336064 Numbers divisible by the maximal exponent in their prime factorization (A051903).

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79
Offset: 1

Views

Author

Amiram Eldar, Jul 07 2020

Keywords

Comments

The asymptotic density of this sequence is A336065 = 0.848957... (Schinzel and Šalát, 1994).

Examples

			4 = 2^2 is a term since A051903(4) = 2 is a divisor of 4.

References

  • József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, chapter 3, p. 331.

Links

Crossrefs

Cf. A051903, A124184, A336065.
A005117 (except for 1) is subsequence.
Similar sequences: A033950, A005349, A006446, A074946, A075592, A007694, A112249, A336063.

Programs

  • Mathematica
    H[1] = 0; H[n_] := Max[FactorInteger[n][[;; , 2]]]; Select[Range[2, 100], Divisible[#, H[#]] &]
  • PARI
    isok(m) = if (m>1, (m % vecmax(factor(m)[,2])) == 0); \\ Michel Marcus, Jul 08 2020

A124438 Numbers that are not divisible by at least one of the (positive) exponents in their prime factorization.

Original entry on oeis.org

8, 9, 25, 32, 40, 45, 49, 56, 63, 64, 75, 81, 88, 96, 99, 104, 117, 121, 125, 128, 136, 147, 152, 153, 162, 169, 171, 175, 184, 200, 207, 224, 225, 232, 243, 245, 248, 250, 261, 275, 279, 280, 288, 289, 296, 315, 320, 325, 328, 333, 343, 344, 352
Offset: 1

Views

Author

Franklin T. Adams-Watters, Dec 16 2006

Keywords

Comments

Except for 1, every member of A124184 is in this sequence. Also, this sequence does not contain any squarefree numbers.

Links

Crossrefs

Cf. A124184.

Programs

  • Mathematica
    Select[Range[400],MemberQ[Divisible[#,FactorInteger[#][[All,2]]],False]&] (* Harvey P. Dale, Mar 25 2018 *)

A336063 Numbers divisible by the minimal exponent in their prime factorization (A051904).

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74
Offset: 1

Views

Author

Amiram Eldar, Jul 07 2020

Keywords

Comments

The asymptotic density of this sequence is 1 (Schinzel and Šalát, 1994).

Examples

			4 = 2^2 is a term since A051904(4) = 2 is a divisor of 4.

References

  • József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, chapter 3, p. 331.

Links

Crossrefs

Cf. A051904, A124184.
A005117 (except for 1) is subsequence.
Similar sequences: A033950, A005349, A006446, A074946, A075592, A007694, A112249, A336064.

Programs

  • Mathematica
    h[1] = 0; h[n_] := Min[FactorInteger[n][[;; , 2]]]; Select[Range[2, 100], Divisible[#, h[#]] &]
Select[Range[2,100],Divisible[#,Min[FactorInteger[#][[All,2]]]]&] (* Harvey P. Dale, Aug 31 2020 *)
  • PARI
    isok(m) = if (m>1, (m % vecmin(factor(m)[,2])) == 0); \\ Michel Marcus, Jul 08 2020
Showing 1-3 of 3 results.

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

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