A366803 Dirichlet convolution of Liouville's lambda with A342001 applied to Doudna sequence: a(n) = A347395(A005940(1+n)).

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

Offset: 0

Author

Antti Karttunen, Oct 26 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A003415, A005940, A008836, A342001, A347395, A366805 (rgs-transform).

Cf. also A347396, A366795, A366801.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A342001(n) = (A003415(n) / A003557(n));
A008836(n) = ((-1)^bigomega(n));
A347395(n) = sumdiv(n,d,A008836(n/d)*A342001(d));
A366803(n) = A347395(A005940(1+n));