A361706 - OEIS

%I #16 Mar 23 2023 15:56:27

%S 2,7,9,19,15,37,21,50,39,65,35,116,45,91,87,134,63,174,71,200,125,155,

%T 87,322,125,197,172,282,113,383,131,349,217,271,213,555,161,311,267,

%U 546,183,555,195,482,402,379,215,857,267,546,369,602,245,768,349,774,421,503,281,1204,287,561,582,875,425

%N Inverse Moebius transform applied twice to primes.

%C Dirichlet convolution of primes with the number of divisors function.

%H Winston de Greef, <a href="/A361706/b361706.txt">Table of n, a(n) for n = 1..10000</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F G.f.: Sum_{i>=1} Sum_{j>=1} prime(i) * x^(i*j) / (1 - x^(i*j)).

%F a(n) = Sum_{d|n} A000005(n/d) * prime(d).

%p a:= (proc(p) proc(n) uses numtheory;

%p        add(p(d), d=divisors(n))

%p      end end@@2)(ithprime):

%p seq(a(n), n=1..100);  # _Alois P. Heinz_, Mar 23 2023

%t Table[Sum[DivisorSigma[0, n/d] Prime[d], {d, Divisors[n]}], {n, 1, 65}]

%o (PARI) a(n) = sumdiv(n, d, numdiv(n/d)*prime(d)); \\ _Michel Marcus_, Mar 23 2023

%Y Cf. A000005, A000040, A007429, A007445, A361707.

%K nonn

%O 1,1

%A _Ilya Gutkovskiy_, Mar 21 2023