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Sum of A126760 and its Dirichlet inverse.
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%I #15 Aug 18 2021 21:43:33

%S 2,0,0,1,0,2,0,1,1,4,0,1,0,6,4,1,0,1,0,2,6,8,0,1,4,10,1,3,0,0,0,1,8,

%T 12,12,1,0,14,10,2,0,0,0,4,2,16,0,1,9,14,12,5,0,1,16,3,14,20,0,2,0,22,

%U 3,1,20,0,0,6,16,12,0,1,0,26,14,7,24,0,0,2,1,28,0,3,24,30,20,4,0,2,30,8,22,32,28,1,0,25,4,9,0,0,0,5,12

%N Sum of A126760 and its Dirichlet inverse.

%C From _Antti Karttunen_, Aug 18 2021: (Start)

%C No negative terms in range 1 .. 2^20.

%C Apparently zeros occur only on (some of the) positions given by A030059, with exceptions for example on n = 70, 105, 110, 130, 154, etc, where a(n) > 0.

%C (End)

%H Antti Karttunen, <a href="/A323882/b323882.txt">Table of n, a(n) for n = 1..20000</a>

%H Antti Karttunen, <a href="/A323882/a323882.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%F a(n) = A126760(n) + A323881(n).

%F For n > 1, a(n) = -Sum_{d|n, 1<d<n} A126760(d) * A323881(n/d). - _Antti Karttunen_, Aug 18 2021

%o (PARI)

%o up_to = 20000;

%o A126760(n) = {n&&n\=3^valuation(n, 3)<<valuation(n, 2); n%3+n\6*2}; \\ From A126760

%o 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 v323881 = DirInverseCorrect(vector(up_to,n,A126760(n)));

%o A323881(n) = v323881[n];

%o A323882(n) = (A126760(n)+A323881(n));

%Y Cf. A030059, A126760, A323881, A323884, A323885, A323887.

%K nonn,look

%O 1,1

%A _Antti Karttunen_, Feb 08 2019