A358769 a(n) = 1 if n is of the form p * m^2, where p is a prime and m is a natural number >= 1, otherwise 0.

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

Offset

1

Comments

Numbers k such that its prime factorization Product_{i} p_i^e_i contains exactly one odd e_i. - Chai Wah Wu, Jun 06 2025

Links

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

Index entries for characteristic functions

Index entries for sequences computed from exponents in factorization of n

Formula

a(n) = A010051(A007913(n)).

a(n) >= A010051(n).

a(n) = A062799(n) mod 2. - Ridouane Oudra, May 07 2025

a(n) = Sum_{d|n} A392285(d). - Ridouane Oudra, Feb 16 2026

Prog

(PARI) A358769(n) = isprime(core(n));
(Python)
from sympy import factorint
def A358769(n): return int(sum(e&1 for e in factorint(n).values())==1) # Chai Wah Wu, Jun 06 2025

Crossrefs

Characteristic function of A229125.

Cf. A007913, A010051, A358770, A062799, A008836, A001221, A392285.

Sequence in context: A284653 A359158 A099104 * A066829 A194664 A285975

Adjacent sequences: A358766 A358767 A358768 * A358770 A358771 A358772

Keyword

nonn

Author

Antti Karttunen, Dec 01 2022

Status

approved