1,2

T(n,k) = 0 if k does not divide n.

n-th row = "n" followed by (n-2) zeros and 1 if n is prime.

Row sums = A140255: (1, 3, 4, 5, 6, 7, 8, 7, 7, 9, 12,...).

Similar to A138618.

T. Tao, Simons Lecture I: Structure and randomness in Fourier analysis and number theory.

Wikipedia, Fundamental theorem of arithmetic.

Triangle by columns, n terms in n-th row; A014963 interleaved with (k-1) zeros. A014963 = (1, 2, 3, 2, 5, 1, 7, 2, 3, 1, 11, 1, 13, 1,...).

a(n) = A014963(A126988).

First few rows of the triangle are:

1;

2, 1;

3, 0, 1;

2, 2, 0, 1;

5, 0, 0, 0, 1;

1, 3, 2, 0, 0, 1;

7, 0, 0, 0, 0, 0, 1;

2, 2, 0, 2, 0, 0, 0, 1;

3, 0, 3, 0, 0, 0, 0, 0, 1;

1, 5, 0, 0, 2, 0, 0, 0, 0, 1;

11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

1, 1, 2, 3, 0, 2, 0, 0, 0, 0, 0, 1;

...

Column 2 = (1, 0, 2, 0, 3, 0, 2, 0, 5, 0, 1, 0, 7,...).

(Excel cell formula) =if(row()>=column(); if(mod(row(); column())=0; lookup(roundup(row()/column(); 0); A000027; A014963); 0); "")

Cf. A140255, A014963.

Row products A000027. [From Mats Granvik (mats.granvik(AT)abo.fi), Oct 08 2009]

Sequence in context: A157929 A071431 A140699 this_sequence A126206 A119709 A120251

Adjacent sequences: A140253 A140254 A140255 this_sequence A140257 A140258 A140259

nonn,tabl

Gary W. Adamson and Mats Granvik (qntmpkt(AT)yahoo.com), May 16 2008, Jun 11 2008