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A366390 Dirichlet inverse of A366389.

%I A366390 #10 Oct 23 2023 08:34:11
%S A366390 1,-2,-3,0,-5,6,-7,0,0,10,-26,0,-22,14,15,0,-17,0,-25,0,21,91,-29,0,6,
%T A366390 77,0,0,-23,-30,-31,0,123,34,-28,0,-82,50,75,0,-74,-42,-106,-156,0,58,
%U A366390 -122,0,-21,-12,51,-132,-86,0,142,0,111,46,-110,0,-94,62,0,0,155,-480,-97,0,93,203,-113,0,-73,287,-66,0,275
%N A366390 Dirichlet inverse of A366389.
%H A366390 Antti Karttunen, <a href="/A366390/b366390.txt">Table of n, a(n) for n = 1..16384</a>
%H A366390 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A366390 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A366389(n/d) * a(d).
%o A366390 (PARI)
%o A366390 A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));
%o A366390 A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2)));
%o A366390 A073675(n) = if(valuation(n,2)%2,n/2,2*n);
%o A366390 A366389(n) = { my(u=A057889(n)); if(!((u-n)%3),u,A073675(u)); };
%o A366390 memoA366390 = Map();
%o A366390 A366390(n) = if(1==n,1,my(v); if(mapisdefined(memoA366390,n,&v), v, v = -sumdiv(n,d,if(d<n,A366389(n/d)*A366390(d),0)); mapput(memoA366390,n,v); (v)));
%Y A366390 Cf. A010872, A030101, A057889, A073675, A366389, A366392 (rgs-transform).
%Y A366390 Cf. also A365711.
%K A366390 sign
%O A366390 1,2
%A A366390 _Antti Karttunen_, Oct 22 2023