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A323896 Sum of binary Gray code A003188 and its Dirichlet inverse, A323895.

%I A323896 #8 Feb 08 2019 21:43:31
%S A323896 2,0,0,9,0,12,0,9,4,42,0,0,0,24,28,27,0,62,0,-15,16,84,0,33,49,66,44,
%T A323896 -6,0,-74,0,45,56,150,56,-4,0,156,44,123,0,118,0,-36,130,168,0,24,16,
%U A323896 -105,100,-27,0,-62,196,69,104,114,0,230,0,96,180,99,154,46,0,-69,112,42,0,186,0,330,-98,-72,112,118,0,39,117,366,0,47
%N A323896 Sum of binary Gray code A003188 and its Dirichlet inverse, A323895.
%H A323896 Antti Karttunen, <a href="/A323896/b323896.txt">Table of n, a(n) for n = 1..16384</a>
%H A323896 Antti Karttunen, <a href="/A323896/a323896.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A323896 a(n) = A003188(n) + A323895(n).
%o A323896 (PARI)
%o A323896 up_to = 65537;
%o A323896 DirInverse(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = -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 A323896 A003188(n) = bitxor(n, n>>1);
%o A323896 v323895 = DirInverse(vector(up_to,n,A003188(n)));
%o A323896 A323895(n) = v323895[n];
%o A323896 A323896(n) = (A003188(n)+A323895(n));
%Y A323896 Cf. A003188, A323895.
%Y A323896 Cf. also A323365, A323412, A323885, A323887, A323894.
%K A323896 sign
%O A323896 1,1
%A A323896 _Antti Karttunen_, Feb 08 2019