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A004199 Table of [ x/y ], where (x,y) = (1,1),(1,2),(2,1),(1,3),(2,2),(3,1),... 1

%I

%S 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,

%T 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,

%U 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

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

%C 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

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

%e Array begins:

%e 1 0 0 0 0 0 0 0 ...

%e 2 1 0 0 0 0 0 0 ...

%e 3 1 1 0 0 0 0 0 ...

%e 4 2 1 1 0 0 0 0 ...

%e 5 2 1 1 1 0 0 0 ...

%e ...

%t (* Array version: *)

%t Grid[Table[Floor[n/k], {n, 14}, {k, 14}]] (* _L. Edson Jeffery_, Aug 31 2014 *)

%t (* Array antidiagonals flattened: *)

%t Flatten[Table[Floor[(n - k + 1)/k], {n, 14}, {k, n}]] (* _L. Edson Jeffery_, Aug 31 2014 *)

%Y Cf. A002541 (antidiagonal sums).

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

%K tabl,nonn

%O 1,3

%A _David W. Wilson_

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Last modified August 8 19:29 EDT 2020. Contains 336298 sequences. (Running on oeis4.)