A046143 Triangle T(n, k) = gcd(2^n-1, 2^k-1), for n>=1 and 1 <= k <= n.

1, 1, 3, 1, 1, 7, 1, 3, 1, 15, 1, 1, 1, 1, 31, 1, 3, 7, 3, 1, 63, 1, 1, 1, 1, 1, 1, 127, 1, 3, 1, 15, 1, 3, 1, 255, 1, 1, 7, 1, 1, 7, 1, 1, 511, 1, 3, 1, 3, 31, 3, 1, 3, 1, 1023, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2047, 1, 3, 7, 15, 1, 63, 1, 15, 7, 3, 1, 4095, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

1,3

Comments

The function T(n,k) = T(k,n) is defined for k > n but only the values for 1 <= k <= n as a triangular array are listed here.

Links

Table of n, a(n) for n=1..90.

Eric Weisstein's World of Mathematics, Greatest Common Divisor

Formula

T(n,k) = 2^gcd(n,k)-1.

Example

Triangle begins
  1;
  1,  3;
  1,  1,  7;
  1,  3,  1, 15;
  1,  1,  1,  1, 31;
  1,  3,  7,  3,  1, 63;

Mathematica

T[ n_, k_] := If[ n < 1 || k < 1, 0, 2^GCD[ n, k] - 1] (* Michael Somos, Jul 18 2011 *)

Prog

(PARI) {T(n, k) = if( n<1 || k<1, 0, 2^gcd(n, k) - 1)} /* Michael Somos, Jul 18 2011 */

Crossrefs

Cf. A000012 (first column), A000225 (right diagonal).

Sequence in context: A053193 A348649 A010273 * A228035 A332538 A071812

Adjacent sequences: A046140 A046141 A046142 * A046144 A046145 A046146

Keyword

nonn,tabl

Author

Eric W. Weisstein

Extensions

Name edited by Michel Marcus, Mar 05 2023

Status

approved