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%I #10 Nov 24 2017 23:16:29
%S 0,1,1,2,1,3,1,2,2,3,1,5,1,3,3,3,1,5,1,5,3,3,1,6,2,3,2,5,1,7,1,4,3,3,
%T 3,8,1,3,3,6,1,7,1,5,5,3,1,8,2,5,3,5,1,6,3,6,3,3,1,11,1,3,5,4,3,7,1,5,
%U 3,7,1,10,1,3,5,5,3,7,1,8,3,3,1,11,3,3,3,6,1,11,3,5,3,3,3,10,1,5,5,8,1,7,1,6,7
%N Number of noncube divisors of n.
%H Antti Karttunen, <a href="/A291208/b291208.txt">Table of n, a(n) for n = 1..16384</a>
%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F G.f.: Sum_{k>=1} x^A007412(k)/(1 - x^A007412(k)).
%F G.f.: Sum_{k>=1} (x^k - x^(k^3))/((1 - x^k)*(1 - x^(k^3))).
%F a(n) = A000005(n) - A061704(n).
%e a(8) = 2 because 8 has 4 divisors {1, 2, 4, 8} among which 2 are noncubes {2, 4}.
%t nmax = 105; Rest[CoefficientList[Series[Sum[(x^k - x^k^3)/((1 - x^k) (1 - x^k^3)), {k, 1, nmax}], {x, 0, nmax}], x]]
%o (PARI) a(n) = sumdiv(n, d, !ispower(d, 3)); \\ _Michel Marcus_, Aug 21 2017
%Y Cf. A000005, A007412, A056595, A061704.
%K nonn
%O 1,4
%A _Ilya Gutkovskiy_, Aug 21 2017
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