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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.

%I A322967 #32 Jan 02 2019 04:36:40
%S A322967 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,
%T A322967 28,36,55,40,25,8,1,9,36,49,91,75,65,30,9,1,10,45,64,140,126,140,80,
%U A322967 36,10,1,11,55,81,204,196,266,175,100,42,11
%N 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.
%H A322967 Seiichi Manyama, <a href="/A322967/b322967.txt">Antidiagonals n = 1..25, flattened</a>
%e A322967 In case of (n,k) = (3,2):
%e A322967   | 1  2  3
%e A322967 --+--------
%e A322967 1 | 1, 2, 3
%e A322967 2 | 2, 4, 6
%e A322967 3 | 3, 6, 9
%e A322967 Distinct products are 1,2,3,4,6,9. So A(3,2) = 6.
%e A322967 Square array begins:
%e A322967    1,  1,   1,   1,   1,   1,    1,    1,    1, ...
%e A322967    2,  3,   4,   5,   6,   7,    8,    9,   10, ...
%e A322967    3,  6,  10,  15,  21,  28,   36,   45,   55, ...
%e A322967    4,  9,  16,  25,  36,  49,   64,   81,  100, ...
%e A322967    5, 14,  30,  55,  91, 140,  204,  285,  385, ...
%e A322967    6, 18,  40,  75, 126, 196,  288,  405,  550, ...
%e A322967    7, 25,  65, 140, 266, 462,  750, 1155, 1705, ...
%e A322967    8, 30,  80, 175, 336, 588,  960, 1485, 2200, ...
%e A322967    9, 36, 100, 225, 441, 784, 1296, 2025, 3025, ...
%t A322967 Table[Length@ Union@ Flatten[TensorProduct @@ ConstantArray[Range@ #, k]] &[n - k + 1], {n, 11}, {k, n, 1, -1}] // Flatten (* _Michael De Vlieger_, Jan 01 2019 *)
%Y A322967 Columns 1-5 give A001477, A027424, A027425, A100437, A284988
%Y A322967 Main diagonal gives A110713.
%K A322967 nonn,tabl
%O A322967 1,3
%A A322967 _Seiichi Manyama_, Dec 31 2018