A126855 Numbers k such that, if k = product{p|k} p^c(k,p), each c(k,p) is a positive integer and each p is a distinct prime, then the smallest prime-power p^c(k, p) is not a power of the smallest prime dividing k.

12, 24, 40, 45, 48, 56, 60, 63, 80, 84, 96, 112, 120, 132, 135, 144, 156, 160, 168, 175, 176, 189, 192, 204, 208, 224, 228, 240, 264, 275, 276, 280, 288, 297, 300, 312, 315, 320, 325, 336, 348, 351, 352, 360, 372, 384, 405, 408, 416, 420, 425, 440, 444, 448

Offset: 1

Author

Leroy Quet, Mar 23 2007

Keywords

• nonn

Comments

The numbers of terms not exceeding 10^k, for k=1,2,...., are 0, 11, 128, 1245, 12474, 124052, 1240434, 12398594, 123976845, 1239840735, ... Apparently this sequence has an asymptotic density 0.1239... - Amiram Eldar, Mar 20 2021

Examples

			3600 is included because 3600 = 2^4 * 3^2 * 5^2 and the smallest prime-power (which is largest prime-power of its prime to divide 3600), 3^2 = 9, is not a power of the smallest prime to divide 3600, which is 2.
		

Links

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

Crossrefs

Cf. A020639, A034684, A102749.

Programs

Mathematica

fQ[n_] := Block[{p = Power @@@ FactorInteger[n]},First[p] != Min[p]];Select[Range[460], fQ] (* Ray Chandler, Mar 25 2007 *)

Extensions

Extended by Ray Chandler, Mar 25 2007