A143151 Triangle read by rows, A051731 * (A020639 * 0^(n-k)), 1<=k<=n.

1, 1, 2, 1, 0, 3, 1, 2, 0, 2, 1, 0, 0, 0, 5, 1, 2, 3, 0, 0, 2, 1, 0, 0, 0, 0, 0, 7, 1, 2, 0, 2, 0, 0, 0, 2, 1, 0, 3, 0, 0, 0, 0, 0, 3, 1, 2, 0, 0, 5, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 1, 2, 3, 2, 0, 2, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 1, 2, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 2

Offset

1,3

Comments

Row sums = A143152: (1, 3, 4, 5, 6, 8, 8, 7, 7, 10, 12, 12, 14, 12,

Links

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

Formula

Triangle read by rows, A051731 * (A020639 * 0^(n-k)), 1<=k<=n; where A020639 = Lpf(n). By rows, least prime factors of the divisors of n, where the divisors of n are recorded in triangle A127093.

Example

First few rows of the triangle are:
  1;
  1, 2;
  1, 0, 3;
  1, 2, 0, 2;
  1, 0, 0, 0, 5;
  1, 2, 3, 0, 0, 2;
  1, 0, 0, 0, 0, 0, 7;
  1, 2, 0, 2, 0, 0, 0, 2;
  1, 0, 3, 0, 0, 0, 0, 0, 3;
  1, 2, 0, 0, 5, 0, 0, 0, 0, 2;
  1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11;
  ...
Row 12 = (1, 2, 3, 2, 0, 2, 0, 0, 0, 0, 0, 2) since the divisors of 12 are shown in row 12 of triangle A127093: (1, 2, 3, 4, 0, 6, 0, 0, 0, 0, 0, 12).
Lpf of these terms = row 12 of A143152.

Crossrefs

Cf. A020639, A127093, A143152.

Sequence in context: A243715 A333661 A143256 * A130106 A127093 A141543

Adjacent sequences: A143148 A143149 A143150 * A143152 A143153 A143154

Keyword

nonn,tabl

Author

Gary W. Adamson & Mats Granvik, Jul 27 2008

Status

approved