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A359602 Sum of A244042 and its Dirichlet inverse, where A244042(n) replaces 2's with 0's in the ternary representation of n.

%I A359602 #10 Jan 11 2023 20:59:51
%S A359602 2,0,0,0,0,0,0,0,9,0,0,24,0,0,18,16,0,0,0,24,6,0,0,0,9,0,27,8,0,60,0,
%T A359602 0,54,0,6,36,0,0,78,80,0,72,0,72,27,0,0,12,1,60,54,104,0,0,54,96,6,0,
%U A359602 0,-72,0,0,9,16,78,24,0,72,18,92,0,0,0,0,-21,8,18,0,0,-84,81,0,0,144,54,0,162,32
%N A359602 Sum of A244042 and its Dirichlet inverse, where A244042(n) replaces 2's with 0's in the ternary representation of n.
%H A359602 Antti Karttunen, <a href="/A359602/b359602.txt">Table of n, a(n) for n = 1..19682</a>
%F A359602 a(n) = A244042(n) + A359601(n).
%F A359602 a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A244042(d) * A359601(n/d).
%o A359602 (PARI)
%o A359602 A244042(n) = fromdigits(apply(x->(x%2), digits(n, 3)), 3);
%o A359602 memoA359601 = Map();
%o A359602 A359601(n) = if(1==n,1,my(v); if(mapisdefined(memoA359601,n,&v), v, v = -sumdiv(n,d,if(d<n,A244042(n/d)*A359601(d),0)); mapput(memoA359601,n,v); (v)));
%o A359602 A359602(n) = (A244042(n)+A359601(n));
%Y A359602 Cf. A244042, A359601.
%Y A359602 Cf. A053850 (positions of odd terms), A353569 (parity of terms).
%K A359602 sign,base,easy
%O A359602 1,1
%A A359602 _Antti Karttunen_, Jan 11 2023