A167990 Elements in A126988 (by row) that are not 1.

0, 2, 0, 3, 0, 0, 4, 2, 0, 0, 5, 0, 0, 0, 0, 6, 3, 2, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 8, 4, 0, 2, 0, 0, 0, 0, 9, 0, 3, 0, 0, 0, 0, 0, 0, 10, 5, 0, 0, 2, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 6, 4, 3, 0, 2, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 7, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Mats Granvik, Nov 16 2009

Keywords

• nonn
• tabl

Comments

GCD of rows is A014963.

Examples

			Table begins:
   0;
   2, 0;
   3, 0, 0;
   4, 2, 0, 0;
   5, 0, 0, 0, 0;
   6, 3, 2, 0, 0, 0;
   7, 0, 0, 0, 0, 0, 0;
   8, 4, 0, 2, 0, 0, 0, 0;
   9, 0, 3, 0, 0, 0, 0, 0, 0;
  10, 5, 0, 0, 2, 0, 0, 0, 0, 0;
  11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
  12, 6, 4, 3, 0, 2, 0, 0, 0, 0, 0, 0;
		

Links

• G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Crossrefs

Cf. A014963, A039653, A126988.

Programs

Magma

[k eq n or (n mod k) ne 0 select 0 else n/k: k in [1..n], n in [1..15]]; // G. C. Greubel, Jan 13 2023

Mathematica

Table[If[k==n || Mod[n, k]!=0, 0, n/k], {n,15}, {k,n}]//Flatten (* G. C. Greubel, Jan 13 2023 *)

SageMath

def A167990(n, k):
    if (k==n or n%k!=0): return 0
    else: return n/k
flatten([[A167990(n, k) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Jan 13 2023

Formula

From G. C. Greubel, Jan 13 2023: (Start)

T(n, k) = 0 if k = n or (n mod k) != 0, otherwise T(n, k) = n/k.

T(n, 1) = n - [n=1].

T(m*n, n) = m, m >= 2.

Sum_{k=1..n} T(n, k) = A039653(n). (End)