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

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

Author

Reinhard Zumkeller, Oct 21 2001

Keywords

• nonn

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

• Amiram Eldar, Table of n, a(n) for n = 1..10000

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