A358227 Parity of A328382(n), where A328382(n) = A276086(n) mod A003415(n), with A003415 the arithmetic derivative and A276086 the primorial base exp-function.

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

Offset

2

Links

Antti Karttunen, Table of n, a(n) for n = 2..100000

Index entries for characteristic functions

Index entries for sequences related to primorial base

Formula

a(n) = A000035(A328382(n)).

For all n >= 2, a(n) <= 1-A358220(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); };
A358227(n) = ((A276086(n)%A003415(n))%2);

Crossrefs

Characteristic function of A358228, whose complement A358229 gives the positions of zeros.

Cf. A000035, A003415, A276086, A328382, A358220.

Cf. also A358224.

Sequence in context: A309766 A354033 A328979 * A284524 A226474 A309768

Adjacent sequences: A358224 A358225 A358226 * A358228 A358229 A358230

Keyword

nonn

Author

Antti Karttunen, Nov 25 2022

Status

approved