A359156 - OEIS

A359156

a(n) = 1 if the odd part of n is squarefree and the number of prime factors of n (with multiplicity) is even, otherwise 0.

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

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OFFSET

COMMENTS

a(n) = 1 if A000265(n) is squarefree and A001222(n) is even, otherwise 0.

LINKS

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

Index entries for characteristic functions.

FORMULA

a(n) = A065043(n) * A353627(n).

a(n) = A353627(n) - A359158(n).

a(n) = [A355689(n) > 0], where [ ] is the Iverson bracket.

Sum_{k=1..n} a(k) ~ (4/Pi^2)*n. - Amiram Eldar, Jan 18 2023