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A365803 Dirichlet inverse of bijective base-3 reverse of n (A263273).

%I A365803 #9 Sep 19 2023 15:32:33
%S A365803 1,-2,-3,0,-7,6,-5,0,0,18,-19,0,-13,-2,21,0,-25,0,-11,-8,15,62,-23,0,
%T A365803 32,26,0,40,-55,-54,-37,-32,57,54,-3,0,-31,-14,39,0,-67,6,-49,-96,0,
%U A365803 58,-61,0,-18,-156,75,0,-79,0,237,-32,33,182,-65,24,-47,74,0,160,123,-186,-41,16,69,230,-77,0,-35,62,-96,144
%N A365803 Dirichlet inverse of bijective base-3 reverse of n (A263273).
%H A365803 Antti Karttunen, <a href="/A365803/b365803.txt">Table of n, a(n) for n = 1..19683</a>
%F A365803 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A263273(n/d) * a(d).
%o A365803 (PARI)
%o A365803 A030102(n) = { my(r=[n%3]); while(0<n\=3, r=concat(n%3, r)); subst(Polrev(r),x,3); };
%o A365803 A263273 = n -> if(!n,n,A030102(n/(3^valuation(n,3))) * (3^valuation(n, 3)));
%o A365803 memoA365803 = Map();
%o A365803 A365803(n) = if(1==n,1,my(v); if(mapisdefined(memoA365803,n,&v), v, v = -sumdiv(n,d,if(d<n,A263273(n/d)*A365803(d),0)); mapput(memoA365803,n,v); (v)));
%Y A365803 Cf. A263273, A323239 (parity of terms), A365804.
%Y A365803 Cf. also A365711.
%K A365803 sign
%O A365803 1,2
%A A365803 _Antti Karttunen_, Sep 19 2023