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.
%I A308813 #47 Apr 12 2025 05:43:04
%S A308813 1,1,1,1,2,1,1,3,2,1,1,4,5,3,1,1,5,10,11,2,1,1,6,17,31,17,4,1,1,7,26,
%T A308813 69,82,39,2,1,1,8,37,131,257,256,65,4,1,1,9,50,223,626,1045,730,139,3,
%U A308813 1,1,10,65,351,1297,3156,4097,2218,261,4,1
%N A308813 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals downwards, where A(n,k) is Sum_{d|n} k^(d-1).
%H A308813 Seiichi Manyama, <a href="/A308813/b308813.txt">Antidiagonals n = 1..140, flattened</a>
%F A308813 G.f. of column k: Sum_{j>=1} x^j/(1 - k*x^j).
%F A308813 T(n, k) = Sum_{d|(k+1)} (n-k-1)^(d-1), with T(n, n) = 1. - _G. C. Greubel_, Jun 26 2024
%e A308813 Square array, A(n,k), begins:
%e A308813 1, 1, 1, 1, 1, 1, 1, ...
%e A308813 1, 2, 3, 4, 5, 6, 7, ...
%e A308813 1, 2, 5, 10, 17, 26, 37, ...
%e A308813 1, 3, 11, 31, 69, 131, 223, ...
%e A308813 1, 2, 17, 82, 257, 626, 1297, ...
%e A308813 1, 4, 39, 256, 1045, 3156, 7819, ...
%e A308813 1, 2, 65, 730, 4097, 15626, 46657, ...
%e A308813 Antidiagonal triangle, T(n,k), begins as:
%e A308813 1;
%e A308813 1, 1;
%e A308813 1, 2, 1;
%e A308813 1, 3, 2, 1;
%e A308813 1, 4, 5, 3, 1;
%e A308813 1, 5, 10, 11, 2, 1;
%e A308813 1, 6, 17, 31, 17, 4, 1;
%e A308813 1, 7, 26, 69, 82, 39, 2, 1;
%e A308813 1, 8, 37, 131, 257, 256, 65, 4, 1;
%e A308813 1, 9, 50, 223, 626, 1045, 730, 139, 3, 1;
%e A308813 1, 10, 65, 351, 1297, 3156, 4097, 2218, 261, 4, 1;
%t A308813 A[n_, k_] := DivisorSum[n, If[k == # - 1 == 0, 1, k^(# - 1)] &];
%t A308813 Table[A[k + 1, n - k - 1], {n, 1, 11}, {k, 0, n - 1}] // Flatten (* _Amiram Eldar_, May 07 2021 *)
%o A308813 (Magma)
%o A308813 A:= func< n,k | (&+[k^(d-1): d in Divisors(n)]) >;
%o A308813 A308813:= func< n,k | A(k+1,n-k-1) >;
%o A308813 [A308813(n,k): k in [0..n-1], n in [1..12]]; // _G. C. Greubel_, Jun 26 2024
%o A308813 (SageMath)
%o A308813 def A(n,k): return sum(k^(j-1) for j in (1..n) if (j).divides(n))
%o A308813 def A308813(n,k): return A(k+1,n-k-1)
%o A308813 flatten([[A308813(n,k) for k in range(n)] for n in range(1,13)]) # _G. C. Greubel_, Jun 26 2024
%Y A308813 Columns k=0..10 give A000012, A000005, A034729, A034730, A339684, A339685, A339686, A339687, A339688, A339689, A113999.
%Y A308813 Row n=1..3 give A000012, A000027(k+1), A002522.
%Y A308813 A(n,n) gives A308814.
%K A308813 nonn,tabl
%O A308813 1,5
%A A308813 _Seiichi Manyama_, Jun 26 2019