A127192 Triangle read by rows: square of A054523.

1, 2, 1, 4, 0, 1, 5, 2, 0, 1, 8, 0, 0, 0, 1, 8, 4, 2, 0, 0, 1, 12, 0, 0, 0, 0, 0, 1, 12, 5, 0, 2, 0, 0, 0, 1, 16, 0, 4, 0, 0, 0, 0, 0, 1, 16, 8, 0, 0, 2, 0, 0, 0, 0, 1, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 20, 8, 5, 4, 0, 2, 0, 0, 0, 0, 0, 1, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 1

Author

Gary W. Adamson, Jan 07 2007

Keywords

• nonn
• tabl

Comments

Row sums = A018804: (1, 3, 5, 8, 9, 15, ...), sum of gcd(k,n) for 1<= k <= n. Left column = A029935: (1, 2, 4, 5, 8, 8, 12, 12, ...). A127192 * d(n) = d(n) * n, or A127192 * A000005 = A038040 = (1, 4, 6, 12, 10, 24, 14, ...).

Column k contains terms of A029935 interspersed with (k-1) zeros.

Examples

			First few rows of the triangle:
   1;
   2, 1;
   4, 0, 1;
   5, 2, 0, 1;
   8, 0, 0, 0, 1;
   8, 4, 2, 0, 0, 1;
  12, 0, 0, 0, 0, 0, 1;
  12, 5, 0, 2, 0, 0, 0, 1;
  16, 0, 4, 0, 0, 0, 0, 0, 1;
  ...
		

Crossrefs

Cf. A000005, A018804, A029935, A038040, A054523.

Extensions

a(20) ff. corrected and more terms from Georg Fischer, May 31 2023