A159936 Triangle read by rows, A051731 * A054533 * transpose(A101688), provided A101688 is read as a square array.

1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 3, 4, 1, 1, 2, 2, 3, 2, 1, 1, 2, 3, 4, 5, 6, 1, 1, 2, 2, 4, 4, 4, 4, 1, 1, 2, 3, 3, 3, 6, 6, 6, 1, 1, 2, 2, 4, 4, 5, 4, 5, 4, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 1, 2, 2, 3, 2, 4, 4, 6, 6, 4, 4, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 1, 2, 2, 4, 4, 6, 6, 7, 6, 7, 6, 7, 6

Offset: 1

Author

Gary W. Adamson, Apr 26 2009

Keywords

• nonn
• tabl

Comments

Row sums = A057661: (1, 2, 4, 6, 11, 11, 22,...). Right border = A000010, phi(n).

Examples

			First few rows of the triangle are as follows:
  1;
  1, 1;
  1, 1, 2;
  1, 1, 2, 2;
  1, 1, 2, 3, 4;
  1, 1, 2, 2, 3, 2;
  1, 1, 2, 3, 4, 5, 6;
  1, 1, 2, 2, 4, 4, 4, 4;
  1, 1, 2, 3, 3, 3, 6, 6, 6;
  1, 1, 2, 2, 4, 4, 5, 4, 5, 4;
  1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10;
  1, 1, 2, 2, 3, 2, 4, 4, 6, 6,  4,  4;
  1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12;
  1, 1, 2, 2, 4, 4, 6, 6, 7, 6,  7,  6,  7, 6;
  1, 1, 2, 3, 3, 3, 5, 4, 3, 5,  9,  8, 10, 9, 8;
  1, 1, 2, 2, 4, 4, 4, 4, 8, 8,  8,  8,  8, 8, 8, 8;
  ...
		

Crossrefs

Cf. A000010, A051731, A054532, A054533, A054534, A054535, A057661, A101688.

Formula

Triangle read by rows, A051731 * A054533 * A000012. A051731 = the inverse Mobius transform. A054533 = the lower left half of the Ramanujan sum table. The operation (* transpose(A101688)) takes partial sums of (A051731 * A054533) starting from the right. [Edited by Petros Hadjicostas, Jul 30 2019]

Extensions

Name edited by Petros Hadjicostas, Jul 30 2019