A373550 a(n) is the parity of the n-th squarefree number.

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

Offset

1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A005117(n) mod 2 = A000035(A005117(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2/3.

Mathematica

Mod[Select[Range[200], SquareFreeQ], 2]

Prog

(PARI) lista(kmax) = for(k = 1, kmax, if(issquarefree(k), print1(k % 2, ", ")));
(Python)
from math import isqrt
from sympy import mobius
def A373550(n):
    def f(x): return n+x-sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
    m, k = n, f(n)
    while m != k:
        m, k = k, f(k)
    return m&1 # Chai Wah Wu, Aug 12 2024

Crossrefs

Cf. A000035, A005117, A039956, A056911, A373549, A373551, A373552.

Sequence in context: A005614 A341753 A267605 * A319843 A309847 A266786

Adjacent sequences: A373547 A373548 A373549 * A373551 A373552 A373553

Keyword

nonn,easy

Author

Amiram Eldar, Jun 09 2024

Status

approved