A014491 a(n) = gcd(n, 2^n - 1).

1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 9, 1, 5, 7, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 9, 1, 1, 1, 5, 1, 21, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 27, 1, 1, 1, 1, 1, 15, 1, 1, 7, 1, 1, 3, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 3, 1, 5, 1, 1, 1, 21, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 3, 1, 1

Offset: 1

Author

Gary M. Mcguire (gmm8n(AT)weyl.math.virginia.edu)

Keywords

• nonn
• easy
• nice

Comments

Also the GCD of the "binary n-th powers", the set of positive integers whose base-2 representation consists of a block of bits repeated n times consecutively. - Jeffrey Shallit, Jan 16 2018

prime(k) for k >= 2 divides a(n) if and only if n is divisible by prime(k)*A014664(k). - Robert Israel, Jan 16 2018

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• Daniel M. Kane, Carlo Sanna, and Jeffrey Shallit, Waring's theorem for binary powers, arXiv:1801.04483 [math.NT], Jan 13 2018.

Crossrefs

Cf. A014664.

Programs

Maple

A014491:=n->igcd(n, 2^n-1); seq(A014491(n), n=1..100); # Wesley Ivan Hurt, Feb 02 2014

Mathematica

Table[GCD[n, 2^n-1], {n, 100}] (* Harvey P. Dale, Mar 14 2013 *)

PARI

a(n) = gcd(n, -1 + 1 << n); \\ Amiram Eldar, Nov 21 2024