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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A380543 Nonsquarefree weak numbers k whose squarefree kernel is a primorial.

Original entry on oeis.org

12, 18, 24, 48, 54, 60, 90, 96, 120, 150, 162, 180, 192, 240, 270, 300, 360, 384, 420, 450, 480, 486, 540, 600, 630, 720, 750, 768, 810, 840, 960, 1050, 1080, 1200, 1260, 1350, 1440, 1458, 1470, 1500, 1536, 1620, 1680, 1890, 1920, 2100, 2160, 2250, 2400, 2430
Offset: 1

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Author

Michael De Vlieger, Jul 15 2025

Keywords

Comments

Numbers in this sequence have the following properties:
The number a(n) is such that rad(a(n))^2 does not divide a(n), i.e., a(n) is not powerful (i.e., in A001694), where rad = A007947.
For i > 1, prime(i) | a(n) implies prime(i-1) | a(n).

Examples

			Table of n, a(n) and prime decomposition for n = 1..12:
 n   a(n)  prime decomposition
------------------------------
 1    12   2^2 * 3
 2    18   2   * 3^2
 3    24   2^3 * 3
 4    48   2^4 * 3
 5    54   2   * 3^3
 6    60   2^2 * 3   * 5
 7    90   2   * 3^2 * 5
 8    96   2^5 * 3
 9   120   2^3 * 3   * 5
10   150   2   * 3   * 5^2
11   162   2   * 3^4
12   180   2^2 * 3^2 * 5
		

Crossrefs

Programs

  • Mathematica
    (* Load Fast Mathematica algorithm for A055932 linked at A377854, then: *)
    rad[x_] := Times @@ FactorInteger[x][[All, 1]]; Select[Union@ Flatten[f[6][[3 ;; -1, 2 ;; -1]] ], ! Divisible[#, rad[#]^2] &]

Formula

Intersection of A055932 and A332785, where A332785 = A052485 \ A005117 = A126706 \ A001694.
The union of this sequence and A369374 is A126706.
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