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

1,2

Comments

The lower triangular array is the multiplication table.

The second row is A073675.

The first superdiagonal and the first subdiagonal are both A002378.

Links

Table of n, a(n) for n=1..78.

Example

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.

Sequence in context: A089913 A257522 A059897 * A325821 A341607 A303719

Adjacent sequences: A385339 A385340 A385341 * A385343 A385344 A385345

Keyword

nonn,tabl

Author

Ali Sada, Jun 26 2025

Status

approved