|
%I #14 May 07 2021 00:53:23
%S 1,2,4,8,18,48,138,440,1440,4884,16806,58848,208024,743044,2674484,
%T 9695296,35357686,129646320,477638718,1767268112,6564120708,
%U 24466283836,91482563662,343059673408,1289904147400,4861946609488
%N Dirichlet convolution of phi(n) with Catalan numbers.
%F a(n) ~ 2^(2*n-2) / (sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Sep 11 2019
%F From _Richard L. Ollerton_, May 06 2021: (Start)
%F a(n) = Sum_{d|n} phi(d)*A000108(n/d) (by definition).
%F a(n) = Sum_{k=1..n} A000108(gcd(n,k)).
%F a(n) = Sum_{k=1..n} A000108(n/gcd(n,k))*phi(gcd(n,k))/phi(n/gcd(n,k)). (End)
%t Table[Sum[CatalanNumber[n/d - 1]*EulerPhi[d], {d, Divisors[n]}], {n, 1, 25}] (* _Vaclav Kotesovec_, Sep 10 2019 *)
%Y Cf. A000010, A000108
%K nonn
%O 1,2
%A _Erich Friedman_
|
