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A309082 a(n) = n - floor(n/2^3) + floor(n/3^3) - floor(n/4^3) + ...

%I A309082 #9 Oct 12 2019 09:16:57
%S A309082 1,2,3,4,5,6,7,7,8,9,10,11,12,13,14,14,15,16,17,18,19,20,21,21,22,23,
%T A309082 25,26,27,28,29,29,30,31,32,33,34,35,36,36,37,38,39,40,41,42,43,43,44,
%U A309082 45,46,47,48,50,51,51,52,53,54,55,56,57,58,57,58,59,60,61,62,63,64,64,65,66,67
%N A309082 a(n) = n - floor(n/2^3) + floor(n/3^3) - floor(n/4^3) + ...
%H A309082 Vaclav Kotesovec, <a href="/A309082/b309082.txt">Table of n, a(n) for n = 1..10000</a>
%F A309082 G.f.: (1/(1 - x)) * Sum_{k>=1} (-1)^(k+1) * x^(k^3)/(1 - x^(k^3)).
%F A309082 a(n) ~ 3*zeta(3)*n/4. - _Vaclav Kotesovec_, Oct 12 2019
%t A309082 Table[Sum[(-1)^(k + 1) Floor[n/k^3], {k, 1, n}], {n, 1, 75}]
%t A309082 nmax = 75; CoefficientList[Series[1/(1 - x) Sum[(-1)^(k + 1) x^(k^3)/(1 - x^(k^3)), {k, 1, Floor[nmax^(1/3)] + 1}], {x, 0, nmax}], x] // Rest
%t A309082 Table[Sum[Boole[IntegerQ[d^(1/3)] && OddQ[d]], {d, Divisors[n]}] - Sum[Boole[IntegerQ[d^(1/3)] && EvenQ[d]], {d, Divisors[n]}], {n, 1, 75}] // Accumulate
%Y A309082 Cf. A013937, A059851, A061704, A309081, A309083.
%K A309082 nonn
%O A309082 1,2
%A A309082 _Ilya Gutkovskiy_, Jul 11 2019