%I #13 Nov 13 2020 10:37:27
%S 4,9,12,18,20,25,28,36,44,45,49,50,52,60,63,64,68,75,76,84,90,92,98,
%T 99,100,116,117,121,124,126,132,140,144,147,148,150,153,156,164,169,
%U 171,172,175,180,188,192,196,198,204,207,212,220,225,228,234,236,242,244
%N Numbers k such that k/A008835(k) is cubefree but not squarefree (A067259), 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 + 2, and none are of the form 4*m + 3.
%C The asymptotic density of this sequence is zeta(4) * (1/zeta(3) - 1/zeta(2)) = Pi^4/(90*zeta(3)) - Pi^2/15 = 0.2424190509... (Cohen, 1963).
%H Amiram Eldar, <a href="/A336594/b336594.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 4 is a term since the largest 4th power dividing 4 is 1, and 4/1 = 4 = 2^2 is cubefree but not squarefree.
%e 64 is a term since the largest 4th power dividing 64 is 16, and 64/16 = 4 = 2^2 is cubefree but not squarefree.
%t Select[Range[250], Max[Mod[FactorInteger[#][[;; , 2]], 4]] == 2 &]
%Y Cf. A002117, A008835, A013661, A013662, A067259, A182358.
%Y Complement of A336593 within A252849.
%Y A030140 is a subsequence.
%K nonn
%O 1,1
%A _Amiram Eldar_, Jul 26 2020