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 A034766 Dirichlet convolution of phi(n) with Catalan numbers. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..26. FORMULA a(n) ~ 2^(2*n-2) / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Sep 11 2019 From Richard L. Ollerton, May 06 2021: (Start) 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) MATHEMATICA Table[Sum[CatalanNumber[n/d - 1]*EulerPhi[d], {d, Divisors[n]}], {n, 1, 25}] (* Vaclav Kotesovec, Sep 10 2019 *) CROSSREFS Cf. A000010, A000108 Sequence in context: A113989 A126757 A369386 * A099785 A333497 A367115 Adjacent sequences: A034763 A034764 A034765 * A034767 A034768 A034769 KEYWORD nonn AUTHOR Erich Friedman STATUS approved

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Last modified February 28 01:44 EST 2024. Contains 370379 sequences. (Running on oeis4.)