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A323884 Sum of A322026 and its Dirichlet inverse.

%I A323884 #7 Feb 08 2019 21:42:33
%S A323884 2,0,0,4,0,12,0,8,9,4,0,8,0,4,6,8,0,4,0,4,6,4,0,0,1,4,15,4,0,-2,0,12,
%T A323884 6,4,2,13,0,4,6,4,0,-2,0,4,5,4,0,22,1,2,6,4,0,7,2,4,6,4,0,8,0,4,5,20,
%U A323884 2,-2,0,4,6,0,0,38,0,4,3,4,2,-2,0,10,13,4,0,8,2,4,6,4,0,16,2,4,6,4,2,28,0,2,5,4,0,-2,0,4,0
%N A323884 Sum of A322026 and its Dirichlet inverse.
%H A323884 Antti Karttunen, <a href="/A323884/b323884.txt">Table of n, a(n) for n = 1..20000</a>
%H A323884 Antti Karttunen, <a href="/A323884/a323884.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A323884 a(n) = A322026(n) + A323883(n).
%o A323884 (PARI)
%o A323884 up_to = 65537;
%o A323884 rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A323884 A007814(n) = valuation(n,2);
%o A323884 A007949(n) = valuation(n,3);
%o A323884 v322026 = rgs_transform(vector(up_to, n, [A007814(n), A007949(n)]));
%o A323884 A322026(n) = v322026[n];
%o A323884 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 A323884 v323883 = DirInverse(v322026);
%o A323884 A323883(n) = v323883[n];
%o A323884 A323884(n) = (A322026(n)+A323883(n));
%Y A323884 Cf. A007814, A007949, A322026, A323882, A323883, A323885.
%K A323884 sign
%O A323884 1,1
%A A323884 _Antti Karttunen_, Feb 08 2019