A358775 a(n) = 1 if the prime factorization of n has an even number of prime factors that sum to an odd number, otherwise 0.

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

Offset

1

Links

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

Index entries for characteristic functions

Formula

a(n) = A065043(n) * A000035(A007814(n)).

a(n) = A065043(n) * (1-A356163(n)).

a(n) = A065043(n) - A353374(n).

Prog

(PARI) A358775(n) = (!(bigomega(n)%2) * (valuation(n, 2)%2));
(PARI) A358775(n) = if(bigomega(n)%2, 0, my(f = factor(n)); 1==((sum(i=1, #f~, f[i, 2]*f[i, 1]))%2));

Crossrefs

Characteristic function of A358776.

Cf. A000035, A007814, A065043, A353374, A356163.

Sequence in context: A011673 A361463 A104853 * A354981 A231600 A347579

Adjacent sequences: A358772 A358773 A358774 * A358776 A358777 A358778

Keyword

nonn

Author

Antti Karttunen, Dec 01 2022

Status

approved