A361017 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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 * A227836 A364042 A033764

Adjacent sequences: A361014 A361015 A361016 * A361018 A361019 A361020

KEYWORD

sign

AUTHOR

Antti Karttunen, Mar 02 2023

STATUS

approved