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A361706 Inverse Moebius transform applied twice to primes.

%I A361706 #16 Mar 23 2023 15:56:27
%S A361706 2,7,9,19,15,37,21,50,39,65,35,116,45,91,87,134,63,174,71,200,125,155,
%T A361706 87,322,125,197,172,282,113,383,131,349,217,271,213,555,161,311,267,
%U A361706 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 A361706 Inverse Moebius transform applied twice to primes.
%C A361706 Dirichlet convolution of primes with the number of divisors function.
%H A361706 Winston de Greef, <a href="/A361706/b361706.txt">Table of n, a(n) for n = 1..10000</a>
%H A361706 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A361706 G.f.: Sum_{i>=1} Sum_{j>=1} prime(i) * x^(i*j) / (1 - x^(i*j)).
%F A361706 a(n) = Sum_{d|n} A000005(n/d) * prime(d).
%p A361706 a:= (proc(p) proc(n) uses numtheory;
%p A361706        add(p(d), d=divisors(n))
%p A361706      end end@@2)(ithprime):
%p A361706 seq(a(n), n=1..100);  # _Alois P. Heinz_, Mar 23 2023
%t A361706 Table[Sum[DivisorSigma[0, n/d] Prime[d], {d, Divisors[n]}], {n, 1, 65}]
%o A361706 (PARI) a(n) = sumdiv(n, d, numdiv(n/d)*prime(d)); \\ _Michel Marcus_, Mar 23 2023
%Y A361706 Cf. A000005, A000040, A007429, A007445, A361707.
%K A361706 nonn
%O A361706 1,1
%A A361706 _Ilya Gutkovskiy_, Mar 21 2023