A369069 Dirichlet convolution of Liouville's lambda (A008836) with 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, 3, 1, 5, 1, 0, 1, 7, 6, -1, 1, 2, 1, 0, 8, 11, 1, 8, 1, 13, 0, 0, 1, 14, 1, 6, 12, 17, 10, 0, 1, 19, 14, 14, 1, 20, 1, 0, 5, 23, 1, -3, 1, 2, 18, 0, 1, 0, 14, 20, 20, 29, 1, 0, 1, 31, 7, -3, 16, 32, 1, 0, 24, 34, 1, 5, 1, 37, 3, 0, 16, 38, 1, -5, 4, 41, 1, 0, 20, 43, 30, 32, 1, 9, 18, 0, 32, 47

Offset

1,6

Comments

In contrast to A347395, this sequence has also nonpositive values after the initial term. It seems that A342090 gives most of the positions of nonpositive terms here, apart from k = 0, 729, 1458, 3645, 5103, 5832, 7290, ..., etc.

Links

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

Formula

a(n) = Sum_{d|n} A008836(n/d) * A083345(d).

Prog

(PARI)
A008836(n) = ((-1)^bigomega(n));
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A369069(n) = sumdiv(n, d, A008836(n/d)*A083345(d));

Crossrefs

Cf. A003415, A008836, A083345, A342090.

Cf. also A347395, A369068.

Sequence in context: A290080 A289617 A035648 * A322821 A213621 A053575

Adjacent sequences: A369066 A369067 A369068 * A369070 A369071 A369072

Keyword

sign

Author

Antti Karttunen, Jan 16 2024

Status

approved