A359601 Dirichlet inverse of A244042, where A244042(n) replaces 2's with 0's in the ternary representation of n.

1, 0, -3, -4, -3, 0, -1, 0, 0, -10, -9, 12, -13, -12, 9, 6, -9, 0, -1, 24, 3, -4, -3, 0, 8, 0, 0, -20, -27, 30, -31, -30, 27, -28, -21, 0, -37, -36, 39, 40, -39, 36, -37, 36, 0, -28, -27, -18, -30, 30, 27, 76, -27, 0, 53, 96, 3, -4, -3, -72, -1, 0, 0, 6, 69, 12, -13, 60, 9, 82, -9, 0, -1, 0, -24, 4, 15

Offset: 1

Author

Antti Karttunen, Jan 11 2023

Keywords

• sign
• base
• easy
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 1..19683

Crossrefs

Cf. A244042, A300821, A359602.

Cf. A056911 (positions of odd terms), A323239 (parity of terms), A337945.

Programs

PARI

A244042(n) = fromdigits(apply(x->(x%2), digits(n, 3)), 3);
memoA359601 = Map();
A359601(n) = if(1==n,1,my(v); if(mapisdefined(memoA359601,n,&v), v, v = -sumdiv(n,d,if(dA244042(n/d)*A359601(d),0)); mapput(memoA359601,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA244042(n/d) * a(d).

a(n) = A359602(n) - A244042(n).