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A309083 a(n) = n - floor(n/2^4) + floor(n/3^4) - floor(n/4^4) + ...

%I A309083 #21 Oct 12 2019 11:16:41
%S A309083 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,15,16,17,18,19,20,21,22,23,24,25,
%T A309083 26,27,28,29,30,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,45,46,
%U A309083 47,48,49,50,51,52,53,54,55,56,57,58,59,60,60,61,62,63,64,65,66,67,68,69,70,71
%N A309083 a(n) = n - floor(n/2^4) + floor(n/3^4) - floor(n/4^4) + ...
%H A309083 Vaclav Kotesovec, <a href="/A309083/b309083.txt">Table of n, a(n) for n = 1..10000</a>
%F A309083 G.f.: (1/(1 - x)) * Sum_{k>=1} (-1)^(k+1) * x^(k^4)/(1 - x^(k^4)).
%F A309083 a(n) ~ 7*zeta(4)*n/8 = 7*Pi^4*n/720. - _Vaclav Kotesovec_, Oct 12 2019
%t A309083 Table[Sum[(-1)^(k + 1) Floor[n/k^4], {k, 1, n}], {n, 1, 75}]
%t A309083 nmax = 75; CoefficientList[Series[1/(1 - x) Sum[(-1)^(k + 1) x^(k^4)/(1 - x^(k^4)), {k, 1, Floor[nmax^(1/4)] + 1}], {x, 0, nmax}], x] // Rest
%t A309083 Table[Sum[Boole[IntegerQ[d^(1/4)] && OddQ[d]], {d, Divisors[n]}] - Sum[Boole[IntegerQ[d^(1/4)] && EvenQ[d]], {d, Divisors[n]}], {n, 1, 75}] // Accumulate
%Y A309083 Cf. A013938, A059851, A063775, A309081, A309082.
%K A309083 nonn
%O A309083 1,2
%A A309083 _Ilya Gutkovskiy_, Jul 11 2019