A361017 Dirichlet inverse of Thue-Morse sequence, A010060.

1, -1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 1, 0, 0, 0, 0, -1, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 1, 0, 0, 0, 0, -1, 0, -1, 1, 0, 0, -1, 1, 0, 0, 2, 0, -1, 0, -1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0

Offset

1,77

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A010060(n/d) * a(d).

Mathematica

a[1] = 1; a[n_] := a[n] = -DivisorSum[n, a[#] * ThueMorse[n/#] &, # < n &]; Array[a, 100] (* Amiram Eldar, Mar 02 2023 *)

Prog

(PARI)
A010060(n) = (hammingweight(n)%2);
memoA361017 = Map();
A361017(n) = if(1==n, 1, my(v); if(mapisdefined(memoA361017, n, &v), v, v = -sumdiv(n, d, if(d<n, A010060(n/d)*A361017(d), 0)); mapput(memoA361017, n, v); (v)));

Crossrefs

Cf. A010060, A361018 (parity of terms).

Sequence in context: A219201 A341979 A331838 * A379129 A227836 A364042

Adjacent sequences: A361014 A361015 A361016 * A361018 A361019 A361020

Keyword

sign

Author

Antti Karttunen, Mar 02 2023

Status

approved