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A346558
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a(n) = Sum_{d|n} phi(n/d) * (2^d - 1).
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0
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1, 4, 9, 20, 35, 78, 133, 280, 531, 1070, 2057, 4212, 8203, 16534, 32865, 65840, 131087, 262818, 524305, 1049740, 2097459, 4196390, 8388629, 16782024, 33554575, 67117102, 134218809, 268452212, 536870939, 1073777010, 2147483677, 4295033440, 8589938775, 17180000318, 34359739085
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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} phi(k) * x^k / ((1 - x^k) * (1 - 2*x^k)).
a(n) = Sum_{k=1..n} (2^gcd(n,k) - 1).
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MATHEMATICA
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Table[Sum[EulerPhi[n/d] (2^d - 1), {d, Divisors[n]}], {n, 1, 35}]
nmax = 35; CoefficientList[Series[Sum[EulerPhi[k] x^k/((1 - x^k) (1 - 2 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, eulerphi(n/d)*(2^d - 1)); \\ Michel Marcus, Sep 17 2021
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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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