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A359814 Dirichlet inverse of A359769, where A359769(n) = A353557(n) - A353556(n). 5
1, 1, 0, 1, 0, 0, 0, 2, -1, 0, 0, 1, 0, 0, -1, 3, 0, -1, 0, 1, -1, 0, 0, 2, -1, 0, 0, 1, 0, -1, 0, 5, -1, 0, -1, -1, 0, 0, -1, 2, 0, -1, 0, 1, 0, 0, 0, 4, -1, -1, -1, 1, 0, 0, -1, 2, -1, 0, 0, -1, 0, 0, 0, 8, -1, -1, 0, 1, -1, -1, 0, -2, 0, 0, 0, 1, -1, -1, 0, 4, 0, 0, 0, -1, -1, 0, -1, 2, 0, 0, -1, 1, -1, 0, -1, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,8
LINKS
FORMULA
a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A359769(n/d) * a(d).
PROG
(PARI)
A353556(n) = ((!(n%2))&&(bigomega(n)%2));
A353557(n) = ((n%2)&&(!(bigomega(n)%2)));
A359769(n) = (A353557(n)-A353556(n));
memoA359814 = Map();
A359814(n) = if(1==n, 1, my(v); if(mapisdefined(memoA359814, n, &v), v, v = -sumdiv(n, d, if(d<n, A359769(n/d)*A359814(d), 0)); mapput(memoA359814, n, v); (v)));
CROSSREFS
Cf. A001222, A353556, A353557, A359769, A359816 (parity of terms).
Cf. also A358777 (Dirichlet inverse of A353557), A359763 [= a(A003961(n))], A359815.
Sequence in context: A000161 A060398 A253242 * A359815 A260649 A122855
KEYWORD
sign
AUTHOR
Antti Karttunen, Jan 15 2023
STATUS
approved

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Last modified July 20 23:17 EDT 2024. Contains 374461 sequences. (Running on oeis4.)