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A159936 Triangle read by rows, A051731 * A054533 * transpose(A101688), provided A101688 is read as a square array. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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: A144434 A322057 A323767 * 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

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Last modified September 28 10:48 EDT 2021. Contains 347714 sequences. (Running on oeis4.)