A306533 - OEIS

%I #6 Feb 22 2019 05:17:11

%S 1,1,4,1,3,9,1,2,5,16,1,2,3,8,25,1,2,3,5,10,36,1,2,3,4,6,14,49,1,2,3,

%T 4,5,7,16,64,1,2,3,4,5,6,8,20,81,1,2,3,4,5,6,7,10,23,100,1,2,3,4,5,6,

%U 7,9,12,27,121,1,2,3,4,5,6,7,8,10,13,29,144,1,2,3,4,5,6,7,8,9,11,14,35,169

%N Square array A(n,k), n >= 1, k >= 0, read by antidiagonals: A(n,k) = Sum_{j=1..n} floor(n/j^k).

%F G.f. of column k (for k > 0): (1/(1 - x)) * Sum_{j>=1} x^(j^k)/(1 - x^(j^k)).

%e Square array begins:

%e    1,   1,  1,  1,  1,  1,  ...

%e    4,   3,  2,  2,  2,  2,  ...

%e    9,   5,  3,  3,  3,  3,  ...

%e   16,   8,  5,  4,  4,  4,  ...

%e   25,  10,  6,  5,  5,  5,  ...

%e   36,  14,  7,  6,  6,  6,  ...

%t Table[Function[k, Sum[Floor[n/j^k], {j, 1, n}]][i - n], {i, 0, 12}, {n, 1, i}] // Flatten

%Y Columns k=0..4 give A000290, A006218, A013936, A013937, A013938.

%Y Cf. A306534.

%K nonn,tabl

%O 1,3

%A _Ilya Gutkovskiy_, Feb 22 2019