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A323899 Dirichlet inverse of A287896 (A001511(n)*A002487(n)).

%I A323899 #6 Feb 12 2019 22:36:43
%S A323899 1,-2,-2,1,-3,4,-3,0,0,6,-5,-2,-5,6,8,0,-5,0,-7,-3,4,10,-7,0,2,10,0,
%T A323899 -3,-7,-16,-5,0,14,10,9,0,-11,14,10,0,-11,-8,-13,-5,-8,14,-9,0,0,-4,8,
%U A323899 -5,-13,0,19,0,18,14,-11,8,-9,10,14,0,23,-28,-11,-5,14,-18,-13,0,-15,22,-20,-7,13,-20,-13,0,2,22,-19,4,9,26,10,0,-17
%N A323899 Dirichlet inverse of A287896 (A001511(n)*A002487(n)).
%H A323899 Antti Karttunen, <a href="/A323899/b323899.txt">Table of n, a(n) for n = 1..16384</a>
%o A323899 (PARI)
%o A323899 up_to = 20000;
%o A323899 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 A323899 A001511(n) = (1+valuation(n,2));
%o A323899 A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
%o A323899 A287896(n) = (A001511(n)*A002487(n));
%o A323899 v323899 = DirInverse(vector(up_to,n,A287896(n)));
%o A323899 A323899(n) = v323899[n];
%Y A323899 Cf. A001511, A002487, A092673, A287896, A317843, A323900.
%K A323899 sign
%O A323899 1,2
%A A323899 _Antti Karttunen_, Feb 12 2019