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

1,1

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

Links

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

Example

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.

Mathematica

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

Crossrefs

Cf. A020639, A034684, A102749.

Sequence in context: A098242 A139406 A140831 * A102749 A085231 A057715

Adjacent sequences: A126852 A126853 A126854 * A126856 A126857 A126858

Keyword

nonn

Author

Leroy Quet, Mar 23 2007

Extensions

Extended by Ray Chandler, Mar 25 2007

Status

approved