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A365713 Dirichlet inverse of reversing binary value of n (A065620).

%I A365713 #8 Sep 19 2023 15:32:29
%S A365713 1,-2,1,0,3,-2,-3,0,8,-6,-7,0,-5,6,11,0,15,-16,-15,0,-19,14,13,0,0,10,
%T A365713 24,0,11,-22,-11,0,17,-30,-49,0,-29,30,19,0,-25,38,25,0,88,-26,-27,0,
%U A365713 -8,0,47,0,19,-48,-61,0,-7,-22,-23,0,-21,22,-56,0,33,-34,-63,0,-35,98,61,0,-57,58,96,0,101,-38,-59,0
%N A365713 Dirichlet inverse of reversing binary value of n (A065620).
%H A365713 Antti Karttunen, <a href="/A365713/b365713.txt">Table of n, a(n) for n = 1..16384</a>
%F A365713 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A065620(n/d) * a(d).
%o A365713 (PARI)
%o A365713 A065620(n, c=1) = sum(i=0, logint(n+!n, 2), if(bittest(n, i), (-1)^c++<<i)); \\ From A065620 by _M. F. Hasler_
%o A365713 memoA365713 = Map();
%o A365713 A365713(n) = if(1==n,1,my(v); if(mapisdefined(memoA365713,n,&v), v, v = -sumdiv(n,d,if(d<n,A065620(n/d)*A365713(d),0)); mapput(memoA365713,n,v); (v)));
%Y A365713 Cf. A065620, A365714.
%Y A365713 Cf. also A355819, A365711.
%K A365713 sign
%O A365713 1,2
%A A365713 _Antti Karttunen_, Sep 19 2023