A355820 a(n) = 1 if A003961(n) and A276086(n) are relatively prime, otherwise 0, where A003961 is fully multiplicative with a(p) = nextprime(p), and A276086 is primorial base exp-function.

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

Offset

1

Links

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

Index entries for characteristic functions

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to primorial base

Formula

a(n) = [1 == gcd(A003961(n), A276086(n))], where [ ] is the Iverson bracket.

a(p) = 1 for all odd primes p.

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A355820(n) = (1==gcd(A003961(n), A276086(n)));
(Python)
from math import prod, gcd
from sympy import nextprime, factorint
def A355820(n):
    k = prod(nextprime(p)**e for p, e in factorint(n).items())
    m, p = 1, 2
    while n:
        n, a = divmod(n, p)
        m *= p**a
        p = nextprime(p)
    return int(gcd(k, m)==1) # Chai Wah Wu, Jul 18 2022

Crossrefs

Cf. A003961, A276086, A355442.

Characteristic function of A355821 (positions of 1's), A355822 (positions of zeros).

Sequence in context: A189215 A285128 A080545 * A099991 A091069 A318608

Adjacent sequences: A355817 A355818 A355819 * A355821 A355822 A355823

Keyword

nonn

Author

Antti Karttunen, Jul 18 2022

Status

approved