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 A328408 G.f. A(x) satisfies: A(x) = A(x^2) + x * (1 + 4*x + x^2) / (1 - x)^4. 1
 1, 9, 27, 73, 125, 243, 343, 585, 729, 1125, 1331, 1971, 2197, 3087, 3375, 4681, 4913, 6561, 6859, 9125, 9261, 11979, 12167, 15795, 15625, 19773, 19683, 25039, 24389, 30375, 29791, 37449, 35937, 44217, 42875, 53217, 50653, 61731, 59319, 73125, 68921, 83349, 79507, 97163, 91125 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA G.f.: Sum_{k>=0} x^(2^k) * (1 + 4*x^(2^k) + x^(2^(k+1))) / (1 - x^(2^k))^4. G.f.: (1/7) * Sum_{k>=1} J_3(2*k) * x^k / (1 - x^k), where J_3() is the Jordan function (A059376). Dirichlet g.f.: zeta(s-3) / (1 - 2^(-s)). a(2*n) = a(n) + 8*n^3, a(2*n+1) = (2*n + 1)^3. a(n) = Sum_{d|n} A209229(n/d) * d^3. Product_{n>=1} (1 + x^n)^a(n) = g.f. for A023872. Sum_{k=1..n} a(k) ~ 4*n^4/15. - Vaclav Kotesovec, Oct 15 2019 MATHEMATICA nmax = 45; CoefficientList[Series[Sum[x^(2^k) (1 + 4 x^(2^k) + x^(2^(k + 1)))/(1 - x^(2^k))^4, {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x] // Rest a[n_] := If[EvenQ[n], a[n/2] + n^3, n^3]; Table[a[n], {n, 1, 45}] Table[DivisorSum[n, Boole[IntegerQ[Log[2, n/#]]] #^3 &], {n, 1, 45}] PROG (MAGMA) [n eq 1 select 1 else IsOdd(n) select n^3 else Self(n div 2)+n^3 :n in [1..45]]; // Marius A. Burtea, Oct 15 2019 CROSSREFS Cf. A000578, A001511, A016755, A023872, A059376, A129527, A209229, A328407. Sequence in context: A011923 A029875 A129957 * A198956 A110205 A319085 Adjacent sequences:  A328405 A328406 A328407 * A328409 A328410 A328411 KEYWORD nonn,mult AUTHOR Ilya Gutkovskiy, Oct 14 2019 STATUS approved

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Last modified December 9 08:20 EST 2019. Contains 329877 sequences. (Running on oeis4.)