A046143 - OEIS

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

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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, 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