A085578 Array read by antidiagonals: T(m,n) is the number of distinct products ij with 1<=i<=m, i<=j<=n, for m>=1, n>=1.

1, 2, 2, 3, 3, 3, 4, 5, 5, 4, 5, 6, 6, 6, 5, 6, 8, 8, 8, 8, 6, 7, 9, 11, 9, 11, 9, 7, 8, 11, 12, 13, 13, 12, 11, 8, 9, 12, 15, 15, 14, 15, 15, 12, 9, 10, 14, 17, 19, 17, 17, 19, 17, 14, 10, 11, 15, 18, 20, 22, 18, 22, 20, 18, 15, 11, 12, 17, 20, 22, 24, 24, 24, 24, 22, 20, 17, 12, 13, 18, 23, 24, 27, 27, 25, 27, 27, 24, 23, 18, 13

Offset: 1

Author

Michael Kleber, Jul 09 2003

Keywords

• nonn
• tabl

Examples

			Array begins:
1 2 3 4 5 6 7 8 9 10 ...
2 3 5 6 8 9 11 12 14 15 ...
3 5 6 8 11 12 15 17 18 20 ...
4 6 8 9 13 15 19 20 22 24 ...
5 8 11 13 14 17 22 24 27 28 ...
		

Crossrefs

A027424 is the main diagonal.

Programs

Maple

T := (m,n) -> nops({seq(seq(i*j, i=1..m),j=1..n)});

Mathematica

T[m_, n_] := Length[Union @@ Table[i*j, {i, m}, {j, n}]]