A373486 a(n) = 1 if A276085(n) is a multiple of A003415(n), otherwise 0, where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Formula

a(n) = [n==1 or A373148(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]));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1, primepi(f[k, 1]-1), prime(i))); };
A373486(n) = (1==n || !(A276085(n)%A003415(n)));

Crossrefs

Characteristic function of A373487.

Cf. A003415, A276085, A373148, A373488.

Sequence in context: A100923 A050073 A266843 * A353491 A120474 A266789

Adjacent sequences: A373483 A373484 A373485 * A373487 A373488 A373489

Keyword

nonn

Author

Antti Karttunen, Jun 09 2024

Status

approved