A369068 Möbius transform of A083345, where A083345(n) = n' / gcd(n,n'), and n' stands for the arithmetic derivative of n, A003415.

0, 1, 1, 0, 1, 3, 1, 2, 1, 5, 1, -1, 1, 7, 6, -1, 1, 1, 1, -1, 8, 11, 1, 5, 1, 13, -1, -1, 1, 14, 1, 3, 12, 17, 10, -1, 1, 19, 14, 9, 1, 20, 1, -1, 4, 23, 1, -3, 1, 1, 18, -1, 1, -3, 14, 13, 20, 29, 1, -6, 1, 31, 6, -2, 16, 32, 1, -1, 24, 34, 1, 1, 1, 37, 2, -1, 16, 38, 1, -5, 3, 41, 1, -8, 20, 43, 30, 21, 1, 4, 18

Offset: 1

Author

Antti Karttunen, Jan 16 2024

Keywords

• sign

Comments

In contrast to A346485, this sequence has also negative values. Compare also to A369069.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A003415, A008683, A083345.

Cf. also A346485, A369069.

Programs

PARI

A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A369068(n) = sumdiv(n,d,moebius(n/d)*A083345(d));

Formula

a(n) = Sum_{d|n} A008683(n/d) * A083345(d).