OFFSET
1,2
COMMENTS
Conjecture 1: T(n,k) is the total number of divisors of the terms that are in the k-th blocks of the first n rows of triangle A176206.
Conjecture 2: the sum of row n equals A284870, the total number of parts in all partitions of all positive integers <= n.
The above conjectures are connected due to the correspondence between divisors and partitions (cf. A336811).
EXAMPLE
Triangle begins:
1;
3, 1;
5, 3, 2;
8, 5, 6, 3;
10, 8, 10, 9, 5;
14, 10, 16, 15, 15, 7;
16, 14, 20, 24, 25, 21, 11;
20, 16, 28, 30, 40, 35, 33, 15;
23, 20, 32, 42, 50, 56, 55, 45, 22;
27, 23, 40, 48, 70, 70, 88, 75, 66, 30;
29, 27, 46, 60, 80, 98, 110, 120, 110, 90, 42;
35, 29, 54, 69, 100, 112, 154, 150, 176, 150, 126, 56;
...
For n = 6 the calculation of every term of row 6 is as follows:
--------------------------
k A000041 T(6,k)
1 1 * 14 = 14
2 1 * 10 = 10
3 2 * 8 = 16
4 3 * 5 = 15
5 5 * 3 = 15
6 7 * 1 = 7
. A006218
--------------------------
The sum of row 6 is 14 + 10 + 16 + 15 + 15 + 7 = 77, equaling A284870(6).
PROG
(PARI) f(n) = sum(k=1, n, n\k); \\ A006218
T(n, k) = f(n-k+1)*numbpart(k-1); \\ Michel Marcus, Jan 15 2021
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Jan 10 2021
STATUS
approved