A359792 a(n) = (-1)^A003415(n), where A003415 is the arithmetic derivative of n.

1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1

Offset

1

Comments

Not multiplicative.

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(n) = (-1)^A165560(n).

a(n) = A358680(n) - A165560(n).

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A359792(n) = ((-1)^A003415(n));

Crossrefs

Cf. A003415, A165560, A358680, A359793 (Dirichlet inverse).

Sequence in context: A359154 A359166 A359581 * A362927 A362928 A071935

Adjacent sequences: A359789 A359790 A359791 * A359793 A359794 A359795

Keyword

sign

Author

Antti Karttunen, Jan 14 2023

Status

approved