A102749 - OEIS

%I #22 Aug 03 2022 04:29:14

%S 12,24,40,45,48,56,63,80,90,96,112,120,126,135,144,160,168,175,176,

%T 180,189,192,208,224,240,252,270,275,280,288,297,315,320,325,336,350,

%U 351,352,360,378,384,405,416,425,448,459,475,480,504,513,525,528,539,540

%N Numbers k such that the largest prime-power dividing k is not a power of the largest prime dividing k.

%C Does this sequence have finite density? - _Franklin T. Adams-Watters_, Aug 29 2006

%C The numbers of terms not exceeding 10^k, for k=1,2,..., are 0, 10, 97, 706, 4779, 31249, 203799, 1322874, 8622492, 56559400, ... Apparently this sequence has an asymptotic density 0. - _Amiram Eldar_, Mar 20 2021

%H Amiram Eldar, <a href="/A102749/b102749.txt">Table of n, a(n) for n = 1..10000</a>

%e 45 is a term because 45 = 3^2*5 and 9 (the largest prime-power dividing 45) is not a power of 5 (the largest prime dividing 45).

%e 144 is a term because its largest prime divisor is 3, but the largest prime power divisor, 16, is not a power of 3.

%t fQ[n_] := Block[{p = Power @@@ FactorInteger[n]},Last[p] != Max[p]];Select[Range[540], fQ] (* _Ray Chandler_, May 11 2007 *)

%Y Cf. A006530, A034699, A126855.

%K nonn

%O 1,1

%A _Leroy Quet_, Feb 09 2005

%E More terms from _Franklin T. Adams-Watters_, Aug 29 2006