OFFSET
1,2
LINKS
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Repunit
FORMULA
G.f.: Sum_{n>=1} a(n)*x^n/(1 - x^n) = x/((1 - x)*(1 - 10*x)).
Dirichlet g.f.: (PolyLog(s,10) - zeta(s))/(9*zeta(s)), where PolyLog() is the polylogarithm function.
a(n) = Sum_{d|n} mu(n/d)*(10^d - 1)/9, where mu() is the Moebius function (A008683).
MATHEMATICA
a[n_] := Sum[MoebiusMu[n/d] (10^d - 1)/9, {d, Divisors[n]}]; Array[a, 21]
PROG
(PARI) a(n) = sumdiv(n, d, moebius(n/d)*(10^d-1)/9); \\ Michel Marcus, Nov 05 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 25 2017
STATUS
approved