A354807 a(n) = 1 if A346241(n) is negative, and 0 otherwise, where A346241 is the Dirichlet inverse of {A003415, arithmetic derivative of n + A063524 (1, 0, 0, 0, ...)}.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Formula

a(n) = [A346241(n) < 0], where [ ] is the Iverson bracket

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
memoA346241 = Map();
A346241(n) = if(1==n, 1, my(v); if(mapisdefined(memoA346241, n, &v), v, v = -sumdiv(n, d, if(d<n, A003415(n/d)*A346241(d), 0)); mapput(memoA346241, n, v); (v)));
A354807(n) = (A346241(n)<0);

Crossrefs

Characteristic function of A354808, whose complement A354809 gives the positions of 0's.

Cf. A003415, A346241, A354806.

Sequence in context: A011584 A011585 A267084 * A011586 A011587 A011588

Adjacent sequences: A354804 A354805 A354806 * A354808 A354809 A354810

Keyword

nonn

Author

Antti Karttunen, Jun 08 2022

Status

approved