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A369455
Dirichlet convolution of A083345 with A055615 (Dirichlet inverse of n), where A083345(n) = (n'/gcd(n,n')) and n' is the arithmetic derivative of n.
1
0, 1, 1, -1, 1, 0, 1, 1, -1, 0, 1, -3, 1, 0, 0, -4, 1, -6, 1, -3, 0, 0, 1, 0, -3, 0, -5, -3, 1, 0, 1, 1, 0, 0, 0, 9, 1, 0, 0, 0, 1, 0, 1, -3, -6, 0, 1, -3, -5, -20, 0, -3, 1, -8, 0, 0, 0, 0, 1, 0, 1, 0, -6, -7, 0, 0, 1, -3, 0, 0, 1, -6, 1, 0, -20, -3, 0, 0, 1, -3, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, -3, 0, 0, 0, 0, 1, -42, -6, 29
OFFSET
1,12
COMMENTS
Dirichlet convolution of this sequence with A000010 (Euler phi) is A369068.
LINKS
FORMULA
a(n) = Sum_{d|n} A055615(n/d)*A083345(d).
PROG
(PARI)
A055615(n) = (n*moebius(n));
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A369455(n) = sumdiv(n, d, A083345(n/d)*A055615(d));
CROSSREFS
KEYWORD
sign
AUTHOR
Antti Karttunen, Jan 27 2024
STATUS
approved