A348416 For n >= 1; a(n) = gcd(n,w(n)) where w(n) is the binary weight of n, A000120(n).

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 3, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 5, 1, 1, 2, 1, 4, 1, 1, 3, 1, 1, 2, 1, 2, 3, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 3, 1, 1, 3

Offset

1,6

Comments

a(n) is even for n in A125592, a(n) = 1 for n in A094387.

Links

Table of n, a(n) for n=1..84.

Formula

a(n) = gcd(n, A000120(n)).

a(n) = A000120(n) if and only if n is in A049445. - Amiram Eldar, Oct 19 2021

Example

n = 6; gcd(6, A000120(6)) = 2, thus a(6) = 2.

Mathematica

Array[GCD[#, Total@ IntegerDigits[#, 2]] &, 105] (* Michael De Vlieger, Oct 19 2021 *)

Prog

(PARI) a(n) = gcd(n, hammingweight(n)); \\ Michel Marcus, Oct 19 2021

Crossrefs

Cf. A000120, A001969, A049445, A094387, A125592.

Sequence in context: A066955 A089048 A329443 * A263025 A184348 A307614

Adjacent sequences: A348413 A348414 A348415 * A348417 A348418 A348419

Keyword

nonn,base

Author

Ctibor O. Zizka, Oct 19 2021

Status

approved