A353557 a(n) = 1 if n is an odd number with an even number of prime factors (counted with multiplicity), otherwise 0.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Jon Maiga, Computer-generated formulas for A353557, Sequence Machine.

Index entries for characteristic functions

Formula

a(n) = A000035(n) * A065043(n).

a(n) = A000035(n) - A353558(n).

a(n) = A065043(n) - A353555(n).

For n >= 1, A353480(n) <= a(n) <= A353374(n).

For n >= 1, a(n) = A059841(A327858(n)). [See comments in the latter sequence]

a(n) = [A166698(n) > 0], where [ ] is the Iverson bracket. - Antti Karttunen, Dec 30 2022

a(n) = A059841(A095112(n)). [From Sequence Machine] - Antti Karttunen, Nov 22 2023

a(n) = A353495(n) + A360109(n). - Antti Karttunen, Feb 05 2024

Prog

(PARI) A353557(n) = ((n%2)&&(!(bigomega(n)%2)));
(Python)
from functools import reduce
from operator import ixor
from sympy import factorint
def A353557(n): return 1&n&(reduce(ixor, factorint(n).values(), 0)^1) # Chai Wah Wu, Dec 21 2022

Crossrefs

Characteristic function of A046337.

Cf. A000035, A001222, A059841, A065043, A095112, A166698, A327858, A353374, A353480, A353555, A353556, A353558, A358777 (Dirichlet inverse), A369257 (inverse Möbius transform).

Cf. also A353495, A360109, A369001.

Sequence in context: A287457 A358777 A359595 * A324917 A369974 A369975

Adjacent sequences: A353554 A353555 A353556 * A353558 A353559 A353560

Keyword

nonn

Author

Antti Karttunen, May 01 2022

Status

approved