%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