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A306533
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Square array A(n,k), n >= 1, k >= 0, read by antidiagonals: A(n,k) = Sum_{j=1..n} floor(n/j^k).
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2
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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, 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, 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
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OFFSET
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1,3
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LINKS
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FORMULA
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G.f. of column k (for k > 0): (1/(1 - x)) * Sum_{j>=1} x^(j^k)/(1 - x^(j^k)).
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EXAMPLE
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Square array begins:
1, 1, 1, 1, 1, 1, ...
4, 3, 2, 2, 2, 2, ...
9, 5, 3, 3, 3, 3, ...
16, 8, 5, 4, 4, 4, ...
25, 10, 6, 5, 5, 5, ...
36, 14, 7, 6, 6, 6, ...
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MATHEMATICA
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Table[Function[k, Sum[Floor[n/j^k], {j, 1, n}]][i - n], {i, 0, 12}, {n, 1, i}] // Flatten
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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