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%I #9 Apr 20 2022 09:58:16
%S 1,-2,-2,1,-2,4,-3,-1,2,2,-4,-3,-3,4,3,0,-2,-10,-6,1,8,4,-7,3,1,-2,-8,
%T -1,-5,-4,-9,-1,14,-10,2,17,-6,4,1,-1,-4,-22,-12,1,-3,4,-13,-1,6,-14,
%U -6,11,-8,28,1,1,19,-10,-16,3,-9,4,-25,-1,10,-42,-18,25,18,0,-19,-17,-6,-14,-12,5,13,12,-21,3,24
%N Dirichlet inverse of A103391, "even fractal sequence".
%H Antti Karttunen, <a href="/A353368/b353368.txt">Table of n, a(n) for n = 1..16384</a>
%F a(1) = 1; a(n) = -Sum_{d|n, d < n} A103391(n/d) * a(d).
%F a(n) = A353369(n) - A103391(n).
%o (PARI)
%o up_to = 65537;
%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 A003602(n) = (n/2^valuation(n, 2)+1)/2; \\ From A003602
%o A103391(n) = if(1==n,1,(1+A003602(n-1)));
%o v353368 = DirInverseCorrect(vector(up_to,n,A103391(n)));
%o A353368(n) = v353368[n];
%Y Cf. A003602, A103391, A353369.
%Y Cf. also A349134, A353366.
%K sign
%O 1,2
%A _Antti Karttunen_, Apr 18 2022
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