A356163 - OEIS

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A356163

a(n) = 1 if sum of prime factors of n (taken with multiplicity) is even, otherwise 0.

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

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OFFSET

LINKS

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

Index entries for characteristic functions

FORMULA

a(n) = A059841(A001414(n)).

a(n) >= A353557(n).

For x, y >= 1, a(x*y) >= a(x) * a(y).

a(x*y) = 1 - a(x) - a(y) + 2*a(x)*a(y). - Robert Israel, Nov 03 2022

a(n) = (1+A359154(n))/2). - Antti Karttunen, Dec 19 2022

a(n) = a(A000265(n)) = A065043(A000265(n)) = A353557(A000265(n)). - Antti Karttunen, Jan 15 2023