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A034767 Dirichlet convolution of phi(n) with Bell numbers. 0
1, 2, 4, 8, 19, 58, 209, 888, 4150, 21170, 115985, 678642, 4213609, 27644652, 190899368, 1382959444, 10480142163, 82864874064, 682076806177, 5832742226266, 51724158235802, 474869816272746, 4506715738447345 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 18 16:20 EDT 2021. Contains 347528 sequences. (Running on oeis4.)