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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.
6
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
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
KEYWORD
sign
AUTHOR
Antti Karttunen, Feb 09 2024
STATUS
approved