A381955 a(n) = A051903(n) mod 2.

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

Offset

1

Comments

Differs from A295316 at n = 1, 72, 108, 200, 288, 360, ... .

Differs from A181183 at n = 1, 32, 36, 72, 96, 100, ... .

Differs from A359473 at n = 1, 32, 72, 96, 108, 160, ... .

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000035(A051903(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 - Sum_{k>=2} (-1)^k * (1 - 1/zeta(k)) = 0.7240832794017729923099... = 1 - A394089.

Example

a(1) = A051903(1) mod 2 = 0 mod 2 = 0.
a(2) = A051903(2) mod 2 = 1 mod 2 = 1.

Mathematica

a[n_] := If[n == 1, 0, Mod[Max[FactorInteger[n][[;; , 2]]], 2]]; Array[a, 100]

Prog

(PARI) a(n) = if(n == 1, 0, vecmax(factor(n)[, 2]) % 2);

Crossrefs

Characteristic function of the complement of A368714.

Cf. A000035, A051903, A381956, A394089.

Cf. A181183, A295316, A359473.

Sequence in context: A105565 A332814 A353788 * A348737 A285418 A344617

Adjacent sequences: A381952 A381953 A381954 * A381956 A381957 A381958

Keyword

nonn,easy

Author

Amiram Eldar, Mar 11 2025

Status

approved