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

%I #13 May 07 2021 00:53:06

%S 1,3,5,9,11,20,19,30,31,42,39,66,49,72,77,90,69,124,79,140,127,132,

%T 101,208,137,170,175,224,135,292,143,260,239,238,257,396,187,272,297,

%U 428,213,478,223,412,445,342,245,604,343,496,415,512,291,636,477,674,475

%N Dirichlet convolution of primes (with 1) with phi(n).

%F From _Richard L. Ollerton_, May 06 2021: (Start)

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

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

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

%o (PARI) pbc(n) = if (n==1, 1, prime(n-1));

%o a(n) = sumdiv(n, d, pbc(d)*eulerphi(n/d)); \\ _Michel Marcus_, Feb 28 2019

%Y Cf. A000010, A008578.

%K nonn

%O 1,2

%A _Erich Friedman_