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

1,2

Comments

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

Links

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

Example

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

Mathematica

q[k_] := Max[Most[FactorInteger[k][[;; , 2]]]] < 2; Select[Range[100], q] (* Amiram Eldar, Mar 19 2025 *)

Prog

(PARI) isok(k) = {my(e = factor(k)[, 2]); #e < 2 || vecmax(e[1..#e-1]) == 1; } \\ Amiram Eldar, Mar 19 2025

Crossrefs

Cf. A005117, A065201, A065202.

Sequence in context: A329138 A334969 A362619 * A342526 A325361 A325397

Adjacent sequences: A065197 A065198 A065199 * A065201 A065202 A065203

Keyword

nonn

Author

Reinhard Zumkeller, Oct 21 2001

Extensions

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

Status

approved