A359464 a(n) = 1 if the total number of 1-bits in the exponents of prime factorization n is even, otherwise 0.

1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 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 exponents in factorization of n.

Formula

a(n) = A059841(A064547(n)).

a(n) = 1 - A092248(A367514(n)). - Amiram Eldar, Oct 02 2024

Mathematica

a[n_] := Boole@ EvenQ[Plus @@ DigitCount[FactorInteger[n][[;; , 2]], 2, 1]]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Oct 02 2024 *)

Prog

(PARI)
A064547(n) = {my(f = factor(n)[, 2]); sum(k=1, #f, hammingweight(f[k])); } \\ From A064547.
A359464(n) = !(A064547(n)%2);
(Python)
from functools import reduce
from operator import ixor
from sympy import factorint
def A359464(n): return reduce(ixor, (d.bit_count() for d in factorint(n).values()), 1)&1 # Chai Wah Wu, Jan 04 2023

Crossrefs

Characteristic function of A000379.

Cf. A059841, A064547, A092248, A359465, A367514.

Sequence in context: A374051 A354927 A173861 * A011746 A071005 A287801

Adjacent sequences: A359461 A359462 A359463 * A359465 A359466 A359467

Keyword

nonn,easy,base

Author

Antti Karttunen, Jan 02 2023

Status

approved