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A347134 a(n) = Sum_{d|n} phi(n/d) * A069359(d), where phi is Euler totient function.

%I A347134 #16 Nov 02 2021 10:27:32
%S A347134 0,1,1,3,1,8,1,8,5,12,1,23,1,16,14,20,1,36,1,35,18,24,1,60,9,28,21,47,
%T A347134 1,87,1,48,26,36,22,103,1,40,30,92,1,119,1,71,66,48,1,148,13,92,38,83,
%U A347134 1,144,30,124,42,60,1,247,1,64,86,112,34,183,1,107,50,183,1,268,1,76,110,119,34,215,1,228,81,84
%N A347134 a(n) = Sum_{d|n} phi(n/d) * A069359(d), where phi is Euler totient function.
%C A347134 Dirichlet convolution of A000010 (Euler totient function phi) with A069359.
%C A347134 Dirichlet convolution of A001221 (omega) with A029935 (the convolution square of Euler phi).
%H A347134 Antti Karttunen, <a href="/A347134/b347134.txt">Table of n, a(n) for n = 1..10000</a>
%H A347134 Antti Karttunen, <a href="/A347134/a347134.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A347134 a(n) = Sum_{d|n} A000010(n/d) * A069359(d)
%F A347134 a(n) = Sum_{d|n} A001221(n/d) * A029935(d).
%F A347134 a(n) = Sum_{k=1..n} A069359(gcd(n,k)). - _Antti Karttunen_, Oct 17 2021
%t A347134 Table[DivisorSum[n,EulerPhi[n/#]*#*DivisorSum[#,1/#&,PrimeQ]&],{n,82}] (* _Giorgos Kalogeropoulos_, Oct 28 2021 *)
%o A347134 (PARI)
%o A347134 A069359(n) = (n*sumdiv(n, d, isprime(d)/d)); \\ From A069359
%o A347134 A347134(n) = sumdiv(n,d,eulerphi(n/d)*A069359(d));
%Y A347134 Cf. A000010, A001221, A069359, A029935.
%Y A347134 Cf. also A347131, A347133, A347135.
%K A347134 nonn
%O A347134 1,4
%A A347134 _Antti Karttunen_, Aug 23 2021