|
%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
|
