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%I A362594 #47 Sep 27 2023 02:43:30
%S A362594 24,40,54,56,88,96,104,120,135,136,152,160,168,184,189,216,224,232,
%T A362594 248,250,264,270,280,296,297,312,328,344,351,352,375,376,378,384,408,
%U A362594 416,424,440,456,459,472,480,486,488,513,520,536,544,552,568,584,594,608,616
%N A362594 Exponentially odd numbers that are neither squarefree nor prime powers.
%C A362594 The asymptotic density of this sequence is A065463 - A059956 = 0.09651509914... . - _Amiram Eldar_, Sep 27 2023
%H A362594 Michael De Vlieger, <a href="/A362594/b362594.txt">Table of n, a(n) for n = 1..10000</a>
%F A362594 This sequence is A126706 INTERSECT A268335.
%F A362594 A268335 = Union(S, T) where S is this sequence and T = {A005117 U A097054} = {A005117 U A246551}.
%e A362594 24 = 2^3 * 3^1 is in this sequence because it has 2 distinct prime factors whose multiplicities are odd and one such multiplicity exceeds 1.
%t A362594 Select[Select[Range[1000], Nor[SquareFreeQ[#], PrimePowerQ[#]] &], Times @@ FactorInteger[#][[All, 1]] == (Sqrt[#] /. (c_ : 1)*a_^(b_ : 0) :> (c*a^b)^2) &]
%Y A362594 Cf. A005117, A097054, A126706, A246551, A268335, A301517.
%Y A362594 Cf. A059956, A065463.
%K A362594 nonn
%O A362594 1,1
%A A362594 _Michael De Vlieger_, Sep 08 2023

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