%I #7 Jul 28 2020 10:31:32
%S 1,2,3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,25,26,28,
%T 29,30,31,32,33,34,35,36,37,38,39,41,42,43,44,45,46,47,48,49,50,51,52,
%U 53,55,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,73,74,75
%N Numbers k such that k/A008835(k) is cubefree, where A008835(k) is the largest 4th power dividing k.
%C Numbers such that none of the exponents in their prime factorization is of the form 4*m + 3.
%C Cohen (1963) proved that for a given number k > 2 the asymptotic density of numbers whose exponents in their prime factorization are not of the forms k*m - 1 is zeta(k)/zeta(k-1). In this sequence k = 4, and therefore its asymptotic density is zeta(4)/zeta(3) = Pi^4/(90*zeta(3)) = 0.9003926776...
%H Amiram Eldar, <a href="/A336592/b336592.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 6 is a term since 6 = 2^1 * 3^1 and 1 is not of the form 4*m + 3.
%e 8 is not a term since 8 = 2^3 and 3 is of the form 4*m + 3.
%t Select[Range[100], Max[Mod[FactorInteger[#][[;; , 2]], 4]] < 3 &]
%Y Cf. A002117, A004709, A008835, A013662.
%K nonn
%O 1,2
%A _Amiram Eldar_, Jul 26 2020