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A004199
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Table of [ x/y ], where (x,y) = (1,1),(1,2),(2,1),(1,3),(2,2),(3,1),...
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1
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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
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1,3
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COMMENTS
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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
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LINKS
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FORMULA
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sum_{k=1..n} a(n-k+1,k) = A002541(n+1).
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EXAMPLE
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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 ...
...
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MATHEMATICA
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(* Array version: *)
(* Array antidiagonals flattened: *)
Flatten[Table[Floor[(n - k + 1)/k], {n, 14}, {k, n}]] (* L. Edson Jeffery, Aug 31 2014 *)
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CROSSREFS
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Cf. A010766 (same sequence as triangle, omitting the zeros).
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KEYWORD
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AUTHOR
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STATUS
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approved
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