cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A306533 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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%I A306533 #6 Feb 22 2019 05:17:11
%S A306533 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,
%T A306533 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,
%U A306533 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
%N A306533 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals: A(n,k) = Sum_{j=1..n} floor(n/j^k).
%F A306533 G.f. of column k (for k > 0): (1/(1 - x)) * Sum_{j>=1} x^(j^k)/(1 - x^(j^k)).
%e A306533 Square array begins:
%e A306533    1,   1,  1,  1,  1,  1,  ...
%e A306533    4,   3,  2,  2,  2,  2,  ...
%e A306533    9,   5,  3,  3,  3,  3,  ...
%e A306533   16,   8,  5,  4,  4,  4,  ...
%e A306533   25,  10,  6,  5,  5,  5,  ...
%e A306533   36,  14,  7,  6,  6,  6,  ...
%t A306533 Table[Function[k, Sum[Floor[n/j^k], {j, 1, n}]][i - n], {i, 0, 12}, {n, 1, i}] // Flatten
%Y A306533 Columns k=0..4 give A000290, A006218, A013936, A013937, A013938.
%Y A306533 Cf. A306534.
%K A306533 nonn,tabl
%O A306533 1,3
%A A306533 _Ilya Gutkovskiy_, Feb 22 2019