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A339687
a(n) = Sum_{d|n} 7^(d-1).
10
1, 8, 50, 351, 2402, 16864, 117650, 823894, 5764851, 40356016, 282475250, 1977343950, 13841287202, 96889128064, 678223075300, 4747562333837, 33232930569602, 232630519768872, 1628413597910450, 11398895225729502, 79792266297729700, 558545864365759264
OFFSET
1,2
LINKS
FORMULA
G.f.: Sum_{k>=1} x^k / (1 - 7*x^k).
G.f.: Sum_{k>=1} 7^(k-1) * x^k / (1 - x^k).
a(n) ~ 7^(n-1). - Vaclav Kotesovec, Jun 05 2021
MATHEMATICA
Table[Sum[7^(d - 1), {d, Divisors[n]}], {n, 1, 22}]
nmax = 22; CoefficientList[Series[Sum[x^k/(1 - 7 x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
PROG
(PARI) a(n) = sumdiv(n, d, 7^(d-1)); \\ Michel Marcus, Dec 13 2020
(Magma)
A339687:= func< n | (&+[7^(d-1): d in Divisors(n)]) >;
[A339687(n): n in [1..40]]; // G. C. Greubel, Jun 25 2024
(SageMath)
def A339687(n): return sum(7^(k-1) for k in (1..n) if (k).divides(n))
[A339687(n) for n in range(1, 41)] # G. C. Greubel, Jun 25 2024
CROSSREFS
Column 7 of A308813.
Sums of the form Sum_{d|n} q^(d-1): A034729 (q=2), A034730 (q=3), A113999 (q=10), A339684 (q=4), A339685 (q=5), A339686 (q=6), this sequence (q=7), A339688 (q=8), A339689 (q=9).
Sequence in context: A357479 A133129 A103458 * A238841 A100310 A124963
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 12 2020
STATUS
approved