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A139703 Nonsquarefree positive integers k such that the largest prime power dividing k is prime.

%I A139703 #19 Jun 26 2025 07:58:28
%S A139703 20,28,44,52,60,68,76,84,88,92,99,104,116,117,124,132,136,140,148,152,
%T A139703 153,156,164,171,172,184,188,198,204,207,212,220,228,232,234,236,244,
%U A139703 248,260,261,264,268,272,276,279,284,292,296,304,306,308,312,316,328
%N A139703 Nonsquarefree positive integers k such that the largest prime power dividing k is prime.
%H A139703 Robert Israel, <a href="/A139703/b139703.txt">Table of n, a(n) for n = 1..10000</a>
%F A139703 This sequence consists of the nonsquarefree terms of A122144.
%e A139703 99 = 3^2 * 11^1. 99 is therefore not squarefree, because it is divisible by 3^2. Also, the largest prime power dividing 99 is 11^1. This is a prime, so 99 is included in the sequence.
%p A139703 filter:= proc(n) local F,t,k;
%p A139703   F:= ifactors(n)[2];
%p A139703   if max(seq(t[2],t=F)) = 1 then return false fi;
%p A139703   k:= max[index]([seq(t[1]^t[2],t=F)]);
%p A139703   F[k,2]=1
%p A139703 end proc:
%p A139703 select(filter, [$2..1000]); # _Robert Israel_, Jan 31 2021
%t A139703 Select[Range[330], Max[(f = FactorInteger[#])[[;;, 2]]] > 1 && Max[Power @@@ f] == f[[-1, 1]] &] (* _Amiram Eldar_, Jun 26 2025 *)
%Y A139703 Intersection of A013929 and A122144.
%K A139703 nonn
%O A139703 1,1
%A A139703 _Leroy Quet_, Jun 13 2008
%E A139703 Extended by _Ray Chandler_, Jul 01 2009