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.

A065200 Numbers of the form m * p^k, with p prime, k >= 0, m squarefree and p > any prime factor of m.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 49, 50, 51, 53, 54, 55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 75, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 91, 93
Offset: 1

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Author

Reinhard Zumkeller, Oct 21 2001

Keywords

Comments

This sequence does not contain any arithmetic progression. The first 24 terms coincide with A053460.

Examples

			a(17) = 18 = 2 * 3^2, whereas A065201(4) = 28 = 2^2 * 7 as 2 < 7.

Links

Crossrefs

Cf. A005117, A065201, A065202.

Programs

  • Mathematica
    q[k_] := Max[Most[FactorInteger[k][[;;, 2]]]] < 2; Select[Range[100], q] (* Amiram Eldar, Mar 19 2025 *)
  • PARI
    isok(k) = {my(e = factor(k)[,2]); #e < 2 || vecmax(e[1..#e-1]) == 1;} \\ Amiram Eldar, Mar 19 2025

Extensions

Edited by Franklin T. Adams-Watters, Oct 27 2006

A053425 Even numbers k such that the 120 points of the 600-cell exactly integrate homogeneous polynomials of degree k.

Original entry on oeis.org

14, 16, 18, 22, 26, 28, 34, 38, 46, 58
Offset: 1

Views

Author

N. J. A. Sloane, Mar 14 2000

Keywords

Links

  • P. Boyvalenkov, D. Danev and P. Kazakov, Indices of spherical codes, in Codes and association schemes (Piscataway, NJ, 1999), 47-57, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 56, Amer. Math. Soc., Providence, RI, 2001.

Crossrefs

Cf. A053460.

A364728 Numbers that are not the sum of admirable numbers (not necessarily distinct).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 45, 46, 47, 48, 49, 51, 53, 55, 57, 58, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101
Offset: 1

Views

Author

Amiram Eldar, Aug 05 2023

Keywords

Comments

First differs from A053460 at n = 39.
Giovanni Resta found that 1003 is the largest number that is not a sum of admirable numbers.

Links

Crossrefs

Cf. A053460, A111592.
Analogous sequence with abundant numbers: A283550.

Programs

  • Mathematica
    admQ[n_] := (ab = DivisorSigma[1, n] - 2 n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2];
With[{adm = Select[Range[1200], admQ]}, Position[Rest[CoefficientList[Series[Product[(1 + x^adm[[k]]), {k, 1, Length[adm]}], {x, 0, adm[[-1]]}], x]], 0] // Flatten]
Showing 1-3 of 3 results.

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

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