A385342 Square array A(n,k) read by descending antidiagonals, where each row n starts with an ordered list of positive integers then we swap A(n,k) with the number in the position A(n, A(n,k*n)).

1, 2, 2, 3, 1, 3, 4, 6, 6, 4, 5, 8, 1, 8, 5, 6, 10, 12, 12, 10, 6, 7, 12, 15, 1, 15, 3, 7, 8, 14, 18, 20, 20, 2, 14, 8, 9, 16, 21, 24, 1, 24, 21, 4, 9, 10, 18, 24, 28, 30, 30, 28, 24, 18, 10, 11, 20, 27, 32, 35, 1, 35, 2, 27, 5, 11, 12, 22, 30, 36, 40, 42, 42, 40, 36, 30, 22, 12

Offset: 1

Author

Ali Sada, Jun 26 2025

Keywords

• nonn
• tabl

Comments

The lower triangular array is the multiplication table.

The second row is A073675.

The first superdiagonal and the first subdiagonal are both A002378.

Examples

			The square array begins:
  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, ...
  2, 1, 6, 8, 10, 3, 14, 4, 18, 5, 22, 24, 26, 7, 30, 32, 34, ...
  3, 6, 1, 12, 15, 2, 21, 24, 27, 30, 33, 4, 39, 42, 5, 48, 51, ...
  4, 8, 12, 1, 20, 24, 28, 2, 36, 40, 44, 3, 52, 56, 60, 64, 68, ...
  5, 10, 15, 20, 1, 30, 35, 40, 45, 2, 55, 60, 65, 70, 3, 80, 85, ...
  6, 12, 18, 24, 30, 1, 42, 48, 54, 60, 66, 2, 78, 84, 90, 96, 102, ...
  7, 14, 21, 28, 35, 42, 1, 56, 63, 70, 77, 84, 91, 2, 105, 112, 119, ...
  8, 16, 24, 32, 40, 48, 56, 1, 72, 80, 88, 96, 104, 112, 120, 2, 136, ...
  9, 18, 27, 36, 45, 54, 63, 72, 1, 90, 99, 108, 117, 126, 135, 144, 153, ...
  10, 20, 30, 40, 50, 60, 70, 80, 90, 1, 110, 120, 130, 140, 150, 160, 170, ...
		

Crossrefs

Cf. A002378, A073675.