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A306533
Square array A(n,k), n >= 1, k >= 0, read by antidiagonals: A(n,k) = Sum_{j=1..n} floor(n/j^k).
2
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
OFFSET
1,3
FORMULA
G.f. of column k (for k > 0): (1/(1 - x)) * Sum_{j>=1} x^(j^k)/(1 - x^(j^k)).
EXAMPLE
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, ...
MATHEMATICA
Table[Function[k, Sum[Floor[n/j^k], {j, 1, n}]][i - n], {i, 0, 12}, {n, 1, i}] // Flatten
CROSSREFS
Columns k=0..4 give A000290, A006218, A013936, A013937, A013938.
Cf. A306534.
Sequence in context: A226574 A331154 A331150 * A331146 A196770 A154182
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Feb 22 2019
STATUS
approved