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

1,2

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.

Links

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

Example

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.

Sequence in context: A016585 A309054 A143316 * A122141 A091604 A200192

Adjacent sequences: A127189 A127190 A127191 * A127193 A127194 A127195

Keyword

nonn,tabl

Author

Gary W. Adamson, Jan 07 2007

Extensions

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

Status

approved