A368997 a(n) = 1 if A342001(n) is even, otherwise 0.

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

Offset

1

Comments

Asymptotic mean of this sequence seems to be about 0.416..., i.e., about twice what it is for A368994.

Links

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

Index entries for characteristic functions

Formula

a(n) = A059841(A003415(n) / A003557(n)) = 1 - A342001(n) mod 2.

A368994(n) <= a(n) <= A358680(n).

From Antti Karttunen, Jun 03 2024: (Start)

a(n) >= A369001(n).

a(n) = A035263(n) * A358680(n) = A059841(A373145(n)). [For a proof, consider A001787]

(End)

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A342001(n) = (A003415(n) / A003557(n));
A368997(n) = !(A342001(n)%2);

Crossrefs

Characteristic function of A368998, whose complement A368999 gives the positions of 0's.

Cf. A001787, A003415, A003557, A035263, A059841, A342001, A358680, A368994, A369001, A373145.

Sequence in context: A353374 A326072 A304362 * A373830 A330682 A230135

Adjacent sequences: A368994 A368995 A368996 * A368998 A368999 A369000

Keyword

nonn

Author

Antti Karttunen, Jan 14 2024

Status

approved