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A034766
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Dirichlet convolution of phi(n) with Catalan numbers.
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0
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1, 2, 4, 8, 18, 48, 138, 440, 1440, 4884, 16806, 58848, 208024, 743044, 2674484, 9695296, 35357686, 129646320, 477638718, 1767268112, 6564120708, 24466283836, 91482563662, 343059673408, 1289904147400, 4861946609488
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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(d)*A000108(n/d) (by definition).
a(n) = Sum_{k=1..n} A000108(gcd(n,k)).
a(n) = Sum_{k=1..n} A000108(n/gcd(n,k))*phi(gcd(n,k))/phi(n/gcd(n,k)). (End)
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MATHEMATICA
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Table[Sum[CatalanNumber[n/d - 1]*EulerPhi[d], {d, Divisors[n]}], {n, 1, 25}] (* Vaclav Kotesovec, Sep 10 2019 *)
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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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