A353374 a(n) = 1 if the prime factorization of n has an even number of prime factors that sum to an even number, otherwise 0.

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

Offset

1

Comments

This is the characteristic function of A345452, see comments there.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Formula

a(n) = A035263(n) * A065043(n).

a(n) = [A008836(n) == +1] * [A001414(n) is even], where [ ] is the Iverson bracket.

a(n) = A065043(n) * A356163(n). - Antti Karttunen, Nov 03 2022

Prog

(PARI) A353374(n) = if(bigomega(n)%2, 0, my(f = factor(n)); 0==((sum(i=1, #f~, f[i, 2]*f[i, 1]))%2));
(PARI) A353374(n) = (!(bigomega(n)%2) && !(valuation(n, 2)%2)); \\ After the function "is" provided in A345452 by David A. Corneth, Jun 24 2021

Crossrefs

Characteristic function of A345452.

Cf. A001222, A001414, A008836, A035263, A065043, A353375, A353376 (inverse Möbius transform), A353377, A353378, A356163.

Cf. also A353331, A353370.

Sequence in context: A227291 A271102 A353800 * A326072 A304362 A368997

Adjacent sequences: A353371 A353372 A353373 * A353375 A353376 A353377

Keyword

nonn

Author

Antti Karttunen, Apr 17 2022

Status

approved