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