A369066 Dirichlet convolution of Liouville's lambda (A008836) with A083345, as reordered by the Doudna sequence.

0, 1, 1, 0, 1, 3, 1, 3, 1, 5, 6, 0, 1, 2, 0, -1, 1, 7, 8, 0, 10, 14, 5, 8, 1, 2, 3, 0, 2, 0, 4, 6, 1, 11, 12, 0, 14, 20, 7, 14, 16, 34, 44, 0, 7, 9, 0, -3, 1, 2, 3, 0, 5, 5, 2, 5, 2, 6, 8, 0, 2, 7, 1, -3, 1, 13, 14, 0, 16, 32, 11, 20, 18, 54, 68, 0, 11, 13, 0, -5, 22, 76, 92, 0, 124, 92, 34, 36, 11, 13, 20, 0, 16

Offset: 0

Author

Antti Karttunen, Jan 16 2024

Keywords

• sign
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384

Crossrefs

Cf. A005940, A008836, A083345, A369067 (rgs-transform), A369069.

Cf. also A366803 (compare the scatter plots).

Programs

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
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));
A369066(n) = A369069(A005940(1+n));

Formula

a(n) = A369069(A005940(1+n)).