Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Apr 18 2022 17:49:20
%S 2,0,0,4,0,8,0,4,4,8,0,4,0,12,8,9,0,0,0,12,12,16,0,16,4,12,0,14,0,12,
%T 0,16,16,8,12,36,0,24,12,20,0,0,0,24,4,28,0,24,9,12,8,38,0,56,16,30,
%U 24,20,0,34,0,36,-8,32,12,-8,0,60,28,36,0,20,0,24,8,44,24,52,0,44,28,16,0,74,8,48,20,44,0,52
%N Sum of A103391 ("even fractal sequence") and its Dirichlet inverse.
%H Antti Karttunen, <a href="/A353369/b353369.txt">Table of n, a(n) for n = 1..16384</a>
%F a(n) = A103391(n) + A353368(n).
%F For n > 1, a(n) = -Sum_{d|n, 1<d<n} A103391(d) * A353368(n/d).
%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];
%o A353369(n) = (A103391(n)+A353368(n));
%Y Cf. A003602, A103391, A353368.
%Y Cf. also A349135, A353367.
%K sign
%O 1,1
%A _Antti Karttunen_, Apr 18 2022