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A339689
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a(n) = Sum_{d|n} 9^(d-1).
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10
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1, 10, 82, 739, 6562, 59140, 531442, 4783708, 43046803, 387427060, 3486784402, 31381119478, 282429536482, 2541866359780, 22876792461604, 205891136878357, 1853020188851842, 16677181742772430, 150094635296999122, 1350851718060419878, 12157665459057460324
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} x^k / (1 - 9*x^k).
G.f.: Sum_{k>=1} 9^(k-1) * x^k / (1 - x^k).
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MATHEMATICA
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Table[Sum[9^(d - 1), {d, Divisors[n]}], {n, 1, 21}]
nmax = 21; CoefficientList[Series[Sum[x^k/(1 - 9 x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
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PROG
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(PARI) a(n) = sumdiv(n, d, 9^(d-1)); \\ Michel Marcus, Dec 13 2020
(Magma)
A339689:= func< n | (&+[9^(d-1): d in Divisors(n)]) >;
(SageMath)
def A339689(n): return sum(9^(k-1) for k in (1..n) if (k).divides(n))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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