OFFSET
1,2
COMMENTS
GCD of rows is A014963.
LINKS
G. C. Greubel, Rows n = 1..50 of the triangle, flattened
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)
EXAMPLE
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;
MATHEMATICA
Table[If[k==n || Mod[n, k]!=0, 0, n/k], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Jan 13 2023 *)
PROG
(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
(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
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Mats Granvik, Nov 16 2009
STATUS
approved