A049790 Triangular array T read by rows: T(n,k) = Sum_{j=1..k} floor(n/floor(k/j)).

1, 2, 3, 3, 4, 7, 4, 6, 9, 11, 5, 7, 11, 13, 18, 6, 9, 14, 16, 22, 24, 7, 10, 16, 18, 25, 27, 34, 8, 12, 18, 22, 29, 31, 39, 43, 9, 13, 21, 24, 32, 35, 44, 47, 55, 10, 15, 23, 27, 37, 39, 49, 53, 61, 66, 11, 16, 25, 29, 40, 42, 53, 57, 66, 71, 82, 12, 18, 28, 33, 44, 48, 59, 64, 74, 79, 91, 94

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• tabl

Examples

			Triangle begins as:
  1;
  2,  3;
  3,  4,  7;
  4,  6,  9, 11;
  5,  7, 11, 13, 18;
  6,  9, 14, 16, 22, 24;
  7, 10, 16, 18, 25, 27, 34;
  8, 12, 18, 22, 29, 31, 39, 43;
		

Links

• G. C. Greubel, Rows n = 1..100 of triangle, flattened

Crossrefs

Cf. A049791, A049792, A049793, A049794, A049795, A049796.

Programs

GAP

Flat(List([1..15], n-> List([1..n], k-> Sum([1..k], j-> Int(n/Int(k/j)) )))); # G. C. Greubel, Dec 09 2019

Magma

[(&+[Floor(n/Floor(k/j)): j in [1..k]]): k in [1..n], n in [1..15]]; // G. C. Greubel, Dec 09 2019

Maple

seq(seq( add(floor(n/floor(k/j)), j=1..k), k=1..n), n=1..15); # G. C. Greubel, Dec 09 2019

Mathematica

Table[Sum[Floor[n/Floor[k/j]], {j, k}], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Dec 09 2019 *)

PARI

T(n,k) = sum(j=1,k, n\(k\j));
for(n=1, 15, for(k=1, n, print1(T(n,k), ", "))) \\ G. C. Greubel, Dec 09 2019

Sage

[[sum(floor(n/floor(k/j)) for j in (1..k)) for k in (1..n)] for n in (1..15)] # G. C. Greubel, Dec 09 2019