A358220 a(n) = 1 if A276086(n) is a multiple of A003415(n), with a(0) = a(1) = 0. Here A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

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

Offset

0

Links

Antti Karttunen, Table of n, a(n) for n = 0..100000

Index entries for characteristic functions

Index entries for sequences related to primorial base

Formula

For n > 1, a(n) = [A328382(n) == 0], where [ ] is the Iverson bracket.

For n > 1, a(n) <= 1-A358227(n).

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A358220(n) = if(n<2, 0, !(A276086(n)%A003415(n)));

Crossrefs

Characteristic function of A358221.

Cf. A003415, A276086, A328382, A358227.

Cf. also A356310.

Sequence in context: A180433 A358771 A165560 * A354874 A014306 A335716

Adjacent sequences: A358217 A358218 A358219 * A358221 A358222 A358223

Keyword

nonn

Author

Antti Karttunen, Nov 23 2022

Status

approved