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A046143
Triangle T(n, k) = gcd(2^n-1, 2^k-1), for n>=1 and 1 <= k <= n.
0
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
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
KEYWORD
nonn,tabl
EXTENSIONS
Name edited by Michel Marcus, Mar 05 2023
STATUS
approved