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A359793
Dirichlet inverse of (-1)^A003415(n), where A003415 is the arithmetic derivative of n.
3
1, 1, 1, 0, 1, 3, 1, -2, 0, 3, 1, 2, 1, 3, 1, -4, 1, 4, 1, 2, 1, 3, 1, -6, 0, 3, 0, 2, 1, 9, 1, -4, 1, 3, 1, 8, 1, 3, 1, -6, 1, 9, 1, 2, 0, 3, 1, -20, 0, 4, 1, 2, 1, 4, 1, -6, 1, 3, 1, 16, 1, 3, 0, 0, 1, 9, 1, 2, 1, 9, 1, -4, 1, 3, 0, 2, 1, 9, 1, -20, 0, 3, 1, 16, 1, 3, 1, -6, 1, 12, 1, 2, 1, 3, 1, -28, 1, 4, 0
OFFSET
1,6
LINKS
FORMULA
a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A359792(n/d) * a(d).
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A359792(n) = ((-1)^A003415(n));
memoA359793 = Map();
A359793(n) = if(1==n, 1, my(v); if(mapisdefined(memoA359793, n, &v), v, v = -sumdiv(n, d, if(d<n, A359792(n/d)*A359793(d), 0)); mapput(memoA359793, n, v); (v)));
CROSSREFS
Cf. A008966, A005117, A013929 (apparently parity of terms, positions of odd terms, and positions of even terms).
Cf. also A359780, A359823.
Sequence in context: A176107 A327852 A190561 * A074735 A074090 A054025
KEYWORD
sign
AUTHOR
Antti Karttunen, Jan 14 2023
STATUS
approved