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

Author

Ctibor O. Zizka, Oct 19 2021

Keywords

• nonn
• base

Comments

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

Examples

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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

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