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A285768
Moebius transform of repunits (A002275).
0
1, 10, 110, 1100, 11110, 110990, 1111110, 11110000, 111111000, 1111099990, 11111111110, 111110998900, 1111111111110, 11111109999990, 111111111099890, 1111111100000000, 11111111111111110, 111111110999889000, 1111111111111111110, 11111111109999998900, 111111111111109999890
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
Sequence in context: A290672 A290417 A289405 * A242162 A144099 A102092
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 25 2017
STATUS
approved