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%I #13 Nov 13 2020 10:37:33
%S 8,24,27,40,54,56,72,88,104,108,120,125,128,135,136,152,168,184,189,
%T 200,216,232,248,250,264,270,280,296,297,312,328,343,344,351,360,375,
%U 376,378,384,392,408,424,432,440,456,459,472,488,500,504,513,520,536,540
%N Numbers k such that k/A008835(k) is cubeful (A036966), where A008835(k) is the largest 4th power dividing k.
%C Numbers such that at least one of the exponents in their prime factorization is of the form 4*m + 3.
%C The asymptotic density of this sequence is 1 - zeta(4)/zeta(3) = 0.0996073223... (Cohen, 1963).
%C The number of divisors of all the terms is divisible by 4.
%H Amiram Eldar, <a href="/A336593/b336593.txt">Table of n, a(n) for n = 1..10000</a>
%H Eckford Cohen, <a href="https://eudml.org/doc/140760">Arithmetical Notes, XIII. A Sequal to Note IV</a>, Elemente der Mathematik, Vol. 18 (1963), pp. 8-11.
%e 8 is a term since 8 = 2^3 and 3 is of the form 4*m + 3.
%t Select[Range[540], Max[Mod[FactorInteger[#][[;; , 2]], 4]] == 3 &]
%Y Complement of A336592.
%Y Complement of A336594 within A252849.
%Y Cf. A002117, A008835, A013662, A036966.
%Y A176297 is a subsequence.
%K nonn
%O 1,1
%A _Amiram Eldar_, Jul 26 2020
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