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A349385 Dirichlet convolution of A048673 with the Dirichlet inverse of A003961, where A003961 is fully multiplicative with a(p) = nextprime(p), and A048673(n) = (1+A003961(n))/2.

%I A349385 #13 Nov 26 2021 16:17:51
%S A349385 1,-1,-2,-1,-3,4,-5,-1,-2,6,-6,4,-8,10,12,-1,-9,4,-11,6,20,12,-14,4,
%T A349385 -3,16,-2,10,-15,-24,-18,-1,24,18,30,4,-20,22,32,6,-21,-40,-23,12,12,
%U A349385 28,-26,4,-5,6,36,16,-29,4,36,10,44,30,-30,-24,-33,36,20,-1,48,-48,-35,18,56,-60,-36,4,-39,40,12,22,60
%N A349385 Dirichlet convolution of A048673 with the Dirichlet inverse of A003961, where A003961 is fully multiplicative with a(p) = nextprime(p), and A048673(n) = (1+A003961(n))/2.
%C A349385 Convolving this with A003973 gives A336840.
%H A349385 Antti Karttunen, <a href="/A349385/b349385.txt">Table of n, a(n) for n = 1..20000</a>
%H A349385 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A349385 a(n) = Sum_{d|n} A048673(n/d) * A346234(d).
%F A349385 a(n) = A349386(n) - A349384(n).
%o A349385 (PARI)
%o A349385 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A349385 A048673(n) = (A003961(n)+1)/2;
%o A349385 A346234(n) = (moebius(n)*A003961(n));
%o A349385 A349385(n) = sumdiv(n,d,A048673(n/d)*A346234(d));
%Y A349385 Cf. A003961, A048673, A346234, A349384 (Dirichlet inverse), A349386 (sum with it).
%Y A349385 Cf. also A003973, A336840.
%K A349385 sign
%O A349385 1,3
%A A349385 _Antti Karttunen_, Nov 17 2021