A034766 Dirichlet convolution of phi(n) with Catalan numbers.

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

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