A359595 Parity of A358777, where A358777 is Dirichlet inverse of the characteristic function of odd numbers with an even number of prime factors (counted with multiplicity).

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

Offset

1

Links

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

Index entries for characteristic functions

Formula

a(n) = A358777(n) mod 2 = A359589(n) mod 2.

A353480(n) <= a(n) <= A353557(n). [See comments in A358777]

Prog

(PARI)
A353557(n) = ((n%2)&&(!(bigomega(n)%2)));
memoA358777 = Map();
A358777(n) = if(1==n, 1, my(v); if(mapisdefined(memoA358777, n, &v), v, v = -sumdiv(n, d, if(d<n, A353557(n/d)*A358777(d), 0)); mapput(memoA358777, n, v); (v)));
A359595(n) = (A358777(n)%2);

Crossrefs

Characteristic function of A359596.

Parity of A358777 and of A359589.

Cf. A353557.

Differs from A353480 at the positions given by A359597: after 1 for the next time at n=135, where a(135) = 1.

Sequence in context: A279760 A287457 A358777 * A353557 A324917 A369974

Adjacent sequences: A359592 A359593 A359594 * A359596 A359597 A359598

Keyword

nonn

Author

Antti Karttunen, Jan 09 2023

Status

approved