A034760 Dirichlet convolution of primes (with 1) with phi(n).

1, 3, 5, 9, 11, 20, 19, 30, 31, 42, 39, 66, 49, 72, 77, 90, 69, 124, 79, 140, 127, 132, 101, 208, 137, 170, 175, 224, 135, 292, 143, 260, 239, 238, 257, 396, 187, 272, 297, 428, 213, 478, 223, 412, 445, 342, 245, 604, 343, 496, 415, 512, 291, 636, 477, 674, 475

Offset: 1

Author

Erich Friedman

Keywords

• nonn

Crossrefs

Cf. A000010, A008578.

Programs

PARI

pbc(n) = if (n==1, 1, prime(n-1));
a(n) = sumdiv(n, d, pbc(d)*eulerphi(n/d)); \\ Michel Marcus, Feb 28 2019

Formula

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

a(n) = Sum_{d|n} A000010(d)*A008578(n/d) (by definition).

a(n) = Sum_{k=1..n} A008578(gcd(n,k)).

a(n) = Sum_{k=1..n} A008578(n/gcd(n,k))*A000010(gcd(n,k))A000010(n/gcd(n,k)). (End)