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

1,6

Comments

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

Links

Table of n, a(n) for n=1..105.

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]

Example

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.

Sequence in context: A322057 A323767 A357824 * A305749 A320748 A320747

Adjacent sequences: A159933 A159934 A159935 * A159937 A159938 A159939

Keyword

nonn,tabl

Author

Gary W. Adamson, Apr 26 2009

Extensions

Name edited by Petros Hadjicostas, Jul 30 2019

Status

approved