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A361017
Dirichlet inverse of Thue-Morse sequence, A010060.
2
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
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
KEYWORD
sign
AUTHOR
Antti Karttunen, Mar 02 2023
STATUS
approved