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A346480 Sum of A250469 and its Dirichlet inverse.

%I A346480 #16 Nov 02 2021 10:29:36
%S A346480 2,0,0,9,0,30,0,27,25,42,0,45,0,66,70,45,0,75,0,99,110,78,0,3,49,102,
%T A346480 125,135,0,60,0,81,130,114,154,-39,0,138,170,15,0,60,0,261,175,174,0,
%U A346480 117,121,231,190,297,0,-225,182,3,230,186,0,-381,0,222,275,189,238,360,0,423,290,216,0,381,0,246,245,459
%N A346480 Sum of A250469 and its Dirichlet inverse.
%H A346480 Antti Karttunen, <a href="/A346480/b346480.txt">Table of n, a(n) for n = 1..10000</a>
%H A346480 <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%F A346480 a(n) = A250469(n) + A346479(n).
%F A346480 a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A250469(d) * A346479(n/d).
%o A346480 (PARI)
%o A346480 up_to = 16384;
%o A346480 DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(d<n, v[n/d]*u[d], 0)))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
%o A346480 v346479 = DirInverseCorrect(vector(up_to,n,A250469(n)));
%o A346480 A346479(n) = v346479[n];
%o A346480 A346480(n) = (A250469(n)+A346479(n));
%o A346480 (PARI) A346480(n) = if(1==n, 2, -sumdiv(n,d,if((1==d)||n==d,0,A250469(d)*A346479(n/d)))); \\ (Demonstrates the convolution formula).
%Y A346480 Cf. A250469, A346479.
%Y A346480 Cf. also A346478.
%K A346480 sign
%O A346480 1,1
%A A346480 _Antti Karttunen_, Jul 30 2021