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A365711 Dirichlet inverse of balanced ternary enumeration of integers (A117966).

%I A365711 #11 Sep 19 2023 15:32:14
%S A365711 1,1,-3,-3,-2,-3,2,-3,0,-14,-8,9,-13,-7,6,6,-5,0,8,0,-6,-11,7,9,15,
%T A365711 -13,0,-60,-26,42,-31,-30,24,-35,-31,0,-37,-19,39,54,-38,21,-34,18,0,
%U A365711 -5,-17,-18,-18,54,15,75,-14,0,58,3,-24,-29,25,0,29,-31,0,-57,71,33,14,-9,-21,-46,22,0,35,-37,-45,-78,2,39
%N A365711 Dirichlet inverse of balanced ternary enumeration of integers (A117966).
%H A365711 Antti Karttunen, <a href="/A365711/b365711.txt">Table of n, a(n) for n = 1..19683</a>
%F A365711 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A117966(n/d) * a(d).
%F A365711 A011655(abs(a(n))) = A359377(n).
%o A365711 (PARI)
%o A365711 A117966(n) = subst(Pol(apply(x->if(x == 2, -1, x), digits(n, 3)), 'x), 'x, 3); \\ From A117966 by _Gheorghe Coserea_
%o A365711 memoA365711 = Map();
%o A365711 A365711(n) = if(1==n,1,my(v); if(mapisdefined(memoA365711,n,&v), v, v = -sumdiv(n,d,if(d<n,A117966(n/d)*A365711(d),0)); mapput(memoA365711,n,v); (v)));
%Y A365711 Cf. A011655, A117966, A359377, A365428, A365712.
%Y A365711 Cf. also A365713, A365803.
%K A365711 sign
%O A365711 1,3
%A A365711 _Antti Karttunen_, Sep 19 2023