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A285768
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Moebius transform of repunits (A002275).
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0
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1, 10, 110, 1100, 11110, 110990, 1111110, 11110000, 111111000, 1111099990, 11111111110, 111110998900, 1111111111110, 11111109999990, 111111111099890, 1111111100000000, 11111111111111110, 111111110999889000, 1111111111111111110, 11111111109999998900, 111111111111109999890
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OFFSET
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1,2
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LINKS
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Eric Weisstein's World of Mathematics, Repunit
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FORMULA
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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).
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MATHEMATICA
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a[n_] := Sum[MoebiusMu[n/d] (10^d - 1)/9, {d, Divisors[n]}]; Array[a, 21]
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PROG
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(PARI) a(n) = sumdiv(n, d, moebius(n/d)*(10^d-1)/9); \\ Michel Marcus, Nov 05 2018
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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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