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A342433
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a(n) = Sum_{k=1..n} gcd(k,n)^(n-1).
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8
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1, 3, 11, 74, 629, 8085, 117655, 2113796, 43059849, 1001955177, 25937424611, 743379914746, 23298085122493, 793811662313709, 29192938251553759, 1152956691126550536, 48661191875666868497, 2185928270773974154773
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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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a(n) = Sum_{d|n} phi(n/d) * d^(n-1).
a(n) = Sum_{d|n} mu(n/d) * d * sigma_(n-2)(d).
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MATHEMATICA
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a[n_] := Sum[GCD[k, n]^(n - 1), {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Mar 12 2021 *)
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PROG
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(PARI) a(n) = sum(k=1, n, gcd(k, n)^(n-1));
(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*d^(n-1));
(PARI) a(n) = sumdiv(n, d, moebius(n/d)*d*sigma(d, n-2));
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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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