A127471 Triangle formed from the matrix product A051731 * A054522 of infinite lower triangular matrices, read by rows.

1, 2, 1, 2, 0, 2, 3, 2, 0, 2, 2, 0, 0, 0, 4, 4, 2, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, 6, 4, 3, 0, 4, 0, 0, 0, 4, 3, 0, 4, 0, 0, 0, 0, 0, 6, 4, 2, 0, 0, 8, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 6, 4, 6, 4, 0, 4, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12

Offset: 1

Author

Gary W. Adamson, Jan 15 2007

Keywords

• nonn
• tabl

Comments

Left column = (1, 2, 2, 3, 2, 4, ...) = d(n), A000005; right border = (1, 1, 2, 2, 4, 2, 6, ...) = phi(n), A000010; row sums = (1, 3, 4, 7, 6, 12, ...) = sigma(n), A000203.

Examples

			First few rows of the triangle:
  1;
  2, 1;
  2, 0, 2;
  3, 2, 0, 2;
  2, 0, 0, 0, 4;
  4, 2, 4, 0, 0, 2;
  2, 0, 0, 0, 0, 0, 6;
  4, 3, 0, 4, 0, 0, 0, 4;
  3, 0, 4, 0, 0, 0, 0, 0, 6;
  4, 2, 0, 0, 8, 0, 0, 0, 0, 4;
  ...
		

Crossrefs

Cf. A000005, A000010, A000203, A051731, A054522.

Extensions

Edited by N. J. A. Sloane, Aug 11 2019

a(49) = 0 inserted and more terms from Georg Fischer, May 29 2023