Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #16 Mar 20 2021 10:57:00
%S 12,24,40,45,48,56,60,63,80,84,96,112,120,132,135,144,156,160,168,175,
%T 176,189,192,204,208,224,228,240,264,275,276,280,288,297,300,312,315,
%U 320,325,336,348,351,352,360,372,384,405,408,416,420,425,440,444,448
%N 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.
%C 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
%H Amiram Eldar, <a href="/A126855/b126855.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%t fQ[n_] := Block[{p = Power @@@ FactorInteger[n]},First[p] != Min[p]];Select[Range[460], fQ] (* _Ray Chandler_, Mar 25 2007 *)
%Y Cf. A020639, A034684, A102749.
%K nonn
%O 1,1
%A _Leroy Quet_, Mar 23 2007
%E Extended by _Ray Chandler_, Mar 25 2007