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

1,2

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.

Links

Table of n, a(n) for n=1..91.

Example

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.

Sequence in context: A335904 A144736 A137423 * A309044 A240312 A339898

Adjacent sequences: A127468 A127469 A127470 * A127472 A127473 A127474

Keyword

nonn,tabl

Author

Gary W. Adamson, Jan 15 2007

Extensions

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

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

Status

approved