A106448 Table of (x+y)/gcd(x,y) where (x,y) runs through the pairs (1,1), (1,2), (2,1), (1,3), (2,2), (3,1), ...

2, 3, 3, 4, 2, 4, 5, 5, 5, 5, 6, 3, 2, 3, 6, 7, 7, 7, 7, 7, 7, 8, 4, 8, 2, 8, 4, 8, 9, 9, 3, 9, 9, 3, 9, 9, 10, 5, 10, 5, 2, 5, 10, 5, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 6, 4, 3, 12, 2, 12, 3, 4, 6, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 7, 14, 7, 14, 7, 2, 7, 14, 7, 14, 7, 14

Offset: 1

Author

Antti Karttunen, May 21 2005

Keywords

• nonn
• tabl

Comments

Can also be viewed as a triangular table T(n,k) (n>=1, 1<=k<=n) read by rows: T(1,1); T(2,1), T(2,2); T(3,1), T(3,2), T(3,3); T(4,1), T(4,2), T(4,3), T(4,4); ... where T(n,k) gives the least value v>0 such that v*k = 0 modulo n+1, i.e., in other words, T(n,k) = (n+1)/gcd(n+1,k).

Examples

			The top left corner of the square array is:
   2  3  4  5  6  7  8  9 10 11 ...
   3  2  5  3  7  4  9  5 11 ...
   4  5  2  7  8  3 10 11 ...
   5  3  7  2  9  5 11 ...
   6  7  8  9  2 11 ...
   7  4  3  5 11 ...
   8  9 10 11 ...
   9  5 11 ...
  10 11 ...
  11 ...
		

Crossrefs

GF(2)[X] analog: A106449. Row 1 is n+1, row 2 is LEFT(LEFT(LEFT(A026741))), row 3 is LEFT^4(A051176). Essentially the same as A054531, but without its right-hand edge of all-1's.

Formula

Equals A003057/A003989.

T(n, k) = numerator((n+k)/n) = numerator((n+k)/k). - Michel Marcus, Dec 29 2013