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A323887 Sum of Per Nørgård's "infinity sequence" (A004718) and its Dirichlet inverse (A323886).

%I A323887 #10 Feb 08 2019 21:42:53
%S A323887 2,0,0,1,0,-4,0,-1,4,0,0,2,0,-6,0,1,0,0,0,0,12,-2,0,-2,0,2,0,3,0,-8,0,
%T A323887 -1,4,0,0,2,0,-6,-4,0,0,10,0,1,16,-4,0,2,9,-6,0,-1,0,0,0,-3,12,4,0,4,
%U A323887 0,-10,-20,1,0,0,0,0,8,-2,0,-2,0,2,12,3,6,-12,0,0,-4,-2,0,1,0,-4,-8,-1,0,16,-6,2,20,-6,0,-2,0,11,0,3,0,-8,0,1,28
%N A323887 Sum of Per Nørgård's "infinity sequence" (A004718) and its Dirichlet inverse (A323886).
%C A323887 The composer Per Nørgård's name is also written in the OEIS as Per Noergaard.
%H A323887 Antti Karttunen, <a href="/A323887/b323887.txt">Table of n, a(n) for n = 1..16384</a>
%H A323887 Antti Karttunen, <a href="/A323887/a323887.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A323887 a(n) = A004718(n) + A323886(n).
%o A323887 (PARI)
%o A323887 up_to = 65537;
%o A323887 A004718list(up_to) = { my(v=vector(up_to)); v[1]=1; v[2]=-1; for(n=3, up_to, v[n] = if(n%2, 1+v[n>>1], -v[n/2])); (v); }; \\ After code in A004718.
%o A323887 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 A323887 v004718 = A004718list(up_to);
%o A323887 A004718(n) = v004718[n];
%o A323887 v323886 = DirInverse(v004718);
%o A323887 A323886(n) = v323886[n];
%o A323887 A323887(n) = (A004718(n)+A323886(n));
%Y A323887 Cf. A004718, A323886.
%Y A323887 Cf. also A323365, A323882, A323885, A323896.
%K A323887 sign
%O A323887 1,1
%A A323887 _Antti Karttunen_, Feb 08 2019