A034767 Dirichlet convolution of phi(n) with Bell numbers.

1, 2, 4, 8, 19, 58, 209, 888, 4150, 21170, 115985, 678642, 4213609, 27644652, 190899368, 1382959444, 10480142163, 82864874064, 682076806177, 5832742226266, 51724158235802, 474869816272746, 4506715738447345

Offset

1,2

Links

Table of n, a(n) for n=1..23.

Formula

From Richard L. Ollerton, May 06 2021: (Start)

a(n) = Sum_{d|n} phi(d)*A000110(n/d) (by definition).

a(n) = Sum_{k=1..n} A000110(gcd(n,k)).

a(n) = Sum_{k=1..n} A000110(n/gcd(n,k))*phi(gcd(n,k))/phi(n/gcd(n,k)). (End)

Mathematica

Table[Sum[BellB[n/d - 1]*EulerPhi[d], {d, Divisors[n]}], {n, 1, 25}] (* Vaclav Kotesovec, Sep 10 2019 *)

Crossrefs

Cf. A000010, A000110

Sequence in context: A128816 A006897 A287025 * A005518 A326997 A014225

Adjacent sequences: A034764 A034765 A034766 * A034768 A034769 A034770

Keyword

nonn

Author

Erich Friedman

Status

approved