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A346478 Sum of A346476 and its Dirichlet inverse.

%I A346478 #10 Oct 16 2021 17:33:12
%S A346478 2,0,0,1,0,2,0,-3,1,6,0,-11,0,6,6,-5,0,-23,0,-29,6,18,0,-3,9,18,-15,
%T A346478 -37,0,-60,0,-9,18,30,18,23,0,30,18,1,0,-84,0,-83,-61,34,0,-13,9,-67,
%U A346478 30,-91,0,45,54,5,30,54,0,75,0,50,-77,-5,54,-184,0,-137,34,-176,0,-13,0,66,-55,-145,54,-188,0,-37,49
%N A346478 Sum of A346476 and its Dirichlet inverse.
%H A346478 Antti Karttunen, <a href="/A346478/b346478.txt">Table of n, a(n) for n = 1..10000</a>
%H A346478 <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%F A346478 a(n) = A346476(n) + A346477(n).
%F A346478 a(1) = 2; and for n > 2, a(n) = -Sum_{d|n, 1<d<n} A346476(n/d) * A346477(d).
%o A346478 (PARI)
%o A346478 up_to = 16384;
%o A346478 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 A346478 A346476(n) = (n+n-A250469(n));
%o A346478 v346477 = DirInverseCorrect(vector(up_to,n,A346476(n)));
%o A346478 A346477(n) = v346477[n];
%o A346478 A346478(n) = (A346476(n)+A346477(n));
%Y A346478 Cf. A000040, A000720, A062234, A250469, A252748, A346476, A346477.
%Y A346478 Cf. also A323911, A346250, A346480.
%K A346478 sign
%O A346478 1,1
%A A346478 _Antti Karttunen_, Jul 30 2021