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A347104 Dirichlet g.f.: primezeta(s-1) * zeta(s-1) / zeta(s).

%I A347104 #10 Aug 24 2021 13:10:01
%S A347104 0,2,3,2,5,7,7,4,6,13,11,10,13,19,22,8,17,18,19,18,32,31,23,20,20,37,
%T A347104 18,26,29,38,31,16,52,49,58,24,37,55,62,36,41,56,43,42,54,67,47,40,42,
%U A347104 60,82,50,53,54,94,52,92,85,59,60,61,91,78,32,112,92,67,66,112,106,71,48,73,109,100
%N A347104 Dirichlet g.f.: primezeta(s-1) * zeta(s-1) / zeta(s).
%C A347104 a(n) is the sum of the prime terms in row n of A050873.
%C A347104 Moebius transform of A328260.
%H A347104 Seiichi Manyama, <a href="/A347104/b347104.txt">Table of n, a(n) for n = 1..10000</a>
%F A347104 a(n) = Sum_{d|n} mu(n/d) * d * omega(d).
%F A347104 a(n) = Sum_{p|n, p prime} p * phi(n/p).
%F A347104 a(n) = Sum_{k=1..n} A010051(gcd(n,k)) * gcd(n,k).
%t A347104 Table[DivisorSum[n, MoebiusMu[n/#] # PrimeNu[#] &], {n, 1, 75}]
%t A347104 Table[DivisorSum[n, # EulerPhi[n/#] &, PrimeQ[#] &], {n, 1, 75}]
%t A347104 Table[Sum[Boole[PrimeQ[GCD[n, k]]] GCD[n, k], {k, 1, n}], {n, 1, 75}]
%o A347104 (PARI) a(n) = sumdiv(n, d, moebius(n/d)*d*omega(d)); \\ _Michel Marcus_, Aug 18 2021
%Y A347104 Cf. A000010, A001221, A008472, A010051, A018804, A050873, A061397, A078439, A117494, A122411, A255655, A328260, A329354.
%K A347104 nonn
%O A347104 1,2
%A A347104 _Ilya Gutkovskiy_, Aug 18 2021