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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.

%I A077593 #9 Jun 01 2025 22:19:06
%S A077593 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,
%T A077593 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,
%U A077593 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
%N 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.
%F A077593 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).
%e A077593 Rows start:
%e A077593  0,0,0,0,0,0...;
%e A077593  1,1,1,1,1,1...;
%e A077593  1,2,3,4,5,6...;
%e A077593  1,3,5,7,9,11...;
%e A077593  1,4,8,13,19,26,...;
%e A077593  ...
%Y A077593 Columns include A057427, A001477, A006218, A061201, A061202, A061203, A061204.
%Y A077593 Rows include (with offsets) A000004, A000012, A000027, A005408, A034856, A052905.
%Y A077593 Cf. A077593.
%K A077593 nonn,tabl
%O A077593 0,9
%A A077593 _Henry Bottomley_, Nov 08 2002