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A339688
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a(n) = Sum_{d|n} 8^(d-1).
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10
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1, 9, 65, 521, 4097, 32841, 262145, 2097673, 16777281, 134221833, 1073741825, 8589967945, 68719476737, 549756076041, 4398046515265, 35184374186505, 281474976710657, 2251799830495305, 18014398509481985, 144115188210078217, 1152921504607109185
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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 - 8*x^k).
G.f.: Sum_{k>=1} 8^(k-1) * x^k / (1 - x^k).
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MATHEMATICA
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Table[Sum[8^(d - 1), {d, Divisors[n]}], {n, 1, 21}]
nmax = 21; CoefficientList[Series[Sum[x^k/(1 - 8 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, 8^(d-1)); \\ Michel Marcus, Dec 13 2020
(Magma)
A339688:= func< n | (&+[8^(d-1): d in Divisors(n)]) >;
(SageMath)
def A339688(n): return sum(8^(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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