A369974 Dirichlet inverse of A369001, where A369001(n) = 1 if n' / gcd(n,n') is even, otherwise 0, and n' stands for the arithmetic derivative of n, A003415.

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

Offset

1,144

Comments

a(144) = 2 is the first term > 1.

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} A369001(n/d) * a(d).

Prog

(PARI)
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A369001(n) = !(A083345(n)%2);
memoA369974 = Map();
A369974(n) = if(1==n, 1, my(v); if(mapisdefined(memoA369974, n, &v), v, v = -sumdiv(n, d, if(d<n, A369001(n/d)*A369974(d), 0)); mapput(memoA369974, n, v); (v)));

Crossrefs

Cf. A083345, A369001, A369975 (parity of terms), A369976 (positions of odd terms).

Agrees paritywise with A369978.

Cf. A358777, A359763, A359773, A359780 for similar sequences.

Sequence in context: A359595 A353557 A324917 * A369975 A369001 A361024

Adjacent sequences: A369971 A369972 A369973 * A369975 A369976 A369977

Keyword

sign

Author

Antti Karttunen, Feb 09 2024

Status

approved