A004199 - OEIS

A004199

Table of [ x/y ], where (x,y) = (1,1),(1,2),(2,1),(1,3),(2,2),(3,1),...

1, 0, 2, 0, 1, 3, 0, 0, 1, 4, 0, 0, 1, 2, 5, 0, 0, 0, 1, 2, 6, 0, 0, 0, 1, 1, 3, 7, 0, 0, 0, 0, 1, 2, 3, 8, 0, 0, 0, 0, 1, 1, 2, 4, 9, 0, 0, 0, 0, 0, 1, 1, 2, 4, 10, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 11, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 12, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 3, 6, 13, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 6, 14

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OFFSET

1,3

COMMENTS

Entry in row n and column k is also the number of multiples of k less than or equal to n, n,k >= 1. - L. Edson Jeffery, Aug 31 2014

LINKS

Table of n, a(n) for n=1..105.

FORMULA

sum_{k=1..n} a(n-k+1,k) = A002541(n+1).

EXAMPLE

Array begins:

1 0 0 0 0 0 0 0 ...

2 1 0 0 0 0 0 0 ...

3 1 1 0 0 0 0 0 ...

4 2 1 1 0 0 0 0 ...

5 2 1 1 1 0 0 0 ...

...

MATHEMATICA

(* Array version: *)

Grid[Table[Floor[n/k], {n, 14}, {k, 14}]] (* L. Edson Jeffery, Aug 31 2014 *)

(* Array antidiagonals flattened: *)

Flatten[Table[Floor[(n - k + 1)/k], {n, 14}, {k, n}]] (* L. Edson Jeffery, Aug 31 2014 *)

CROSSREFS

Cf. A002541 (antidiagonal sums).

Cf. A010766 (same sequence as triangle, omitting the zeros).

Sequence in context: A128132 A127701 A158821 * A062283 A136493 A338849

Adjacent sequences: A004196 A004197 A004198 * A004200 A004201 A004202

KEYWORD

tabl,nonn

AUTHOR

David W. Wilson

STATUS

approved