A359469 a(n) = A353459(n) mod 2.

0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 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 indices in prime factorization

Formula

For all n >= 1, a(n) = a(A003961(n)) = a(A348717(n)).

Prog

(PARI)
A353457(n) = { my(f=factor(n)); prod(i=1, #f~, if(!(primepi(f[i, 1])%2), 1, if(f[i, 2]==1, -1, 0))); };
A353458(n) = { my(f=factor(n)); prod(i=1, #f~, if(primepi(f[i, 1])%2, 1, if(f[i, 2]==1, -1, 0))); };
A353459(n) = (A353457(n)+A353458(n));
A359469(n) = (A353459(n)%2);
(Python)
from functools import reduce
from operator import iand
from sympy import factorint, primepi
def A359469(n):
    f = [(primepi(p)&1, int(e==1)) for p, e in factorint(n).items()]
    return reduce(iand, (e for p, e in f if not p), 1)^reduce(iand, (e for p, e in f if p), 1) # Chai Wah Wu, Jan 06 2023

Crossrefs

Characteristic function of A359470.

Cf. A003961, A348717, A353457, A353458, A353459.

Differs from A359466 and A359467 for the first time at n=100, as here a(100) = 1.

Sequence in context: A345952 A359466 A359467 * A107078 A341613 A163533

Adjacent sequences: A359466 A359467 A359468 * A359470 A359471 A359472

Keyword

nonn

Author

Antti Karttunen, Jan 04 2023

Status

approved