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A089341 Numbers k with lpf(k) < gpf(k) < 2*lpf(k), where lpf = A020639, gpf = A006530.

%I A089341 #14 May 16 2025 07:29:22
%S A089341 6,12,15,18,24,35,36,45,48,54,72,75,77,91,96,108,135,143,144,162,175,
%T A089341 187,192,209,216,221,225,245,247,288,299,323,324,375,384,391,405,432,
%U A089341 437,486,493,527,539,551,576,589,637,648,667,675,703,713,768,847,851
%N A089341 Numbers k with lpf(k) < gpf(k) < 2*lpf(k), where lpf = A020639, gpf = A006530.
%C A089341 A081306 without prime powers.
%H A089341 Reinhard Zumkeller, <a href="/A089341/b089341.txt">Table of n, a(n) for n = 1..10000</a>
%H A089341 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SmoothNumber.html">Smooth Number</a>.
%F A089341 A046665(a(n)) < A020639(a(n)).
%t A089341 q[k_] := Module[{p = FactorInteger[k][[;;, 1]]}, Length[p] > 1 && p[[-1]] < 2*p[[1]]]; Select[Range[1000], q] (* _Amiram Eldar_, May 16 2025 *)
%o A089341 (Haskell)
%o A089341 a089341 n = a089341_list !! (n-1)
%o A089341 a089341_list = filter (\x -> a006530 x < 2 * a020639 x) a024619_list
%o A089341 -- _Reinhard Zumkeller_, Sep 29 2014
%o A089341 (PARI) isok(k) = if(k == 1, 0, my(p = factor(k)[,1], np = #p);  np > 1 && p[np] < 2*p[1]); \\ _Amiram Eldar_, May 16 2025
%Y A089341 Cf. A005279, A006530, A020639, A046665, A081306.
%Y A089341 Subsequence of A024619.
%K A089341 nonn
%O A089341 1,1
%A A089341 _Reinhard Zumkeller_, Jan 03 2004