A322967 - OEIS

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

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OFFSET

1,3

LINKS

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

EXAMPLE

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, ...

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 *)

CROSSREFS

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

Main diagonal gives A110713.

Sequence in context: A225281 A057145 A134394 * A284855 A074909 A135278

Adjacent sequences: A322964 A322965 A322966 * A322968 A322969 A322970

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, Dec 31 2018

STATUS

approved