A322967 Square array A(n,k), n >= 1, k >= 1, read by antidiagonals, where A(n,k) is the number of distinct products Product_{j=1..k} b_j with 1 <= b_j<= n.

1, 1, 2, 1, 3, 3, 1, 4, 6, 4, 1, 5, 10, 9, 5, 1, 6, 15, 16, 14, 6, 1, 7, 21, 25, 30, 18, 7, 1, 8, 28, 36, 55, 40, 25, 8, 1, 9, 36, 49, 91, 75, 65, 30, 9, 1, 10, 45, 64, 140, 126, 140, 80, 36, 10, 1, 11, 55, 81, 204, 196, 266, 175, 100, 42, 11

Offset: 1

Author

Seiichi Manyama, Dec 31 2018

Keywords

• nonn
• tabl

Examples

			In case of (n,k) = (3,2):
  | 1  2  3
--+--------
1 | 1, 2, 3
2 | 2, 4, 6
3 | 3, 6, 9
Distinct products are 1,2,3,4,6,9. So A(3,2) = 6.
Square array begins:
   1,  1,   1,   1,   1,   1,    1,    1,    1, ...
   2,  3,   4,   5,   6,   7,    8,    9,   10, ...
   3,  6,  10,  15,  21,  28,   36,   45,   55, ...
   4,  9,  16,  25,  36,  49,   64,   81,  100, ...
   5, 14,  30,  55,  91, 140,  204,  285,  385, ...
   6, 18,  40,  75, 126, 196,  288,  405,  550, ...
   7, 25,  65, 140, 266, 462,  750, 1155, 1705, ...
   8, 30,  80, 175, 336, 588,  960, 1485, 2200, ...
   9, 36, 100, 225, 441, 784, 1296, 2025, 3025, ...
		

Links

• Seiichi Manyama, Antidiagonals n = 1..25, flattened

Crossrefs

Columns 1-5 give A001477, A027424, A027425, A100437, A284988

Main diagonal gives A110713.

Programs

Mathematica

Table[Length@ Union@ Flatten[TensorProduct @@ ConstantArray[Range@ #, k]] &[n - k + 1], {n, 11}, {k, n, 1, -1}] // Flatten (* Michael De Vlieger, Jan 01 2019 *)