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

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, -13, 0, -60, -26, 42, -31, -30, 24, -35, -31, 0, -37, -19, 39, 54, -38, 21, -34, 18, 0, -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

Offset: 1

Author

Antti Karttunen, Sep 19 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A011655, A117966, A359377, A365428, A365712.

Cf. also A365713, A365803.

Programs

PARI

A117966(n) = subst(Pol(apply(x->if(x == 2, -1, x), digits(n, 3)), 'x), 'x, 3); \\ From A117966 by Gheorghe Coserea
memoA365711 = Map();
A365711(n) = if(1==n,1,my(v); if(mapisdefined(memoA365711,n,&v), v, v = -sumdiv(n,d,if(dA117966(n/d)*A365711(d),0)); mapput(memoA365711,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA117966(n/d) * a(d).

A011655(abs(a(n))) = A359377(n).