A077593 Table by antidiagonals where T(n,k) = Sum_{i=1..n} T(floor(n/i),k-1) starting with T(n,0)=1 if n>0 and T(0,0)=0.

0, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 3, 1, 0, 1, 4, 5, 4, 1, 0, 1, 5, 7, 8, 5, 1, 0, 1, 6, 9, 13, 10, 6, 1, 0, 1, 7, 11, 19, 16, 14, 7, 1, 0, 1, 8, 13, 26, 23, 25, 16, 8, 1, 0, 1, 9, 15, 34, 31, 39, 28, 20, 9, 1, 0, 1, 10, 17, 43, 40, 56, 43, 38, 23, 10, 1, 0, 1, 11, 19, 53, 50, 76, 61, 63

Offset: 0

Author

Henry Bottomley, Nov 08 2002

Keywords

• nonn
• tabl

Examples

			Rows start:
 0,0,0,0,0,0...;
 1,1,1,1,1,1...;
 1,2,3,4,5,6...;
 1,3,5,7,9,11...;
 1,4,8,13,19,26,...;
 ...
		

Crossrefs

Columns include A057427, A001477, A006218, A061201, A061202, A061203, A061204.

Rows include (with offsets) A000004, A000012, A000027, A005408, A034856, A052905.

Cf. A077593.

Formula

T(n, k) = T(n-1, k) + A077592(n, k). Writing m as Sum_{i} p_i^e_i, T(n, k) = Sum_{m=1..n} Product_{i} C(k+e_i-1, e_i).