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 A343656 #28 May 17 2021 05:02:25
%S A343656 1,1,1,1,2,1,1,3,2,1,1,4,3,3,1,1,5,4,5,2,1,1,6,5,7,3,4,1,1,7,6,9,4,9,
%T A343656 2,1,1,8,7,11,5,16,3,4,1,1,9,8,13,6,25,4,7,3,1,1,10,9,15,7,36,5,10,5,
%U A343656 4,1,1,11,10,17,8,49,6,13,7,9,2,1,1,12,11,19,9,64,7,16,9,16,3,6,1
%N A343656 Array read by antidiagonals where A(n,k) is the number of divisors of n^k.
%C A343656 First differs from A343658 at A(4,2) = 5, A343658(4,2) = 6.
%C A343656 As a triangle, T(n,k) = number of divisors of k^(n-k).
%H A343656 Seiichi Manyama, <a href="/A343656/b343656.txt">Antidiagonals n = 1..140, flattened</a>
%F A343656 A(n,k) = A000005(A009998(n,k)), where A009998(n,k) = n^k is the interpretation as an array.
%F A343656 A(n,k) = Sum_{d|n} k^omega(d). - _Seiichi Manyama_, May 15 2021
%e A343656 Array begins:
%e A343656 k=0 k=1 k=2 k=3 k=4 k=5 k=6 k=7
%e A343656 n=1: 1 1 1 1 1 1 1 1
%e A343656 n=2: 1 2 3 4 5 6 7 8
%e A343656 n=3: 1 2 3 4 5 6 7 8
%e A343656 n=4: 1 3 5 7 9 11 13 15
%e A343656 n=5: 1 2 3 4 5 6 7 8
%e A343656 n=6: 1 4 9 16 25 36 49 64
%e A343656 n=7: 1 2 3 4 5 6 7 8
%e A343656 n=8: 1 4 7 10 13 16 19 22
%e A343656 n=9: 1 3 5 7 9 11 13 15
%e A343656 Triangle begins:
%e A343656 1
%e A343656 1 1
%e A343656 1 2 1
%e A343656 1 3 2 1
%e A343656 1 4 3 3 1
%e A343656 1 5 4 5 2 1
%e A343656 1 6 5 7 3 4 1
%e A343656 1 7 6 9 4 9 2 1
%e A343656 1 8 7 11 5 16 3 4 1
%e A343656 1 9 8 13 6 25 4 7 3 1
%e A343656 1 10 9 15 7 36 5 10 5 4 1
%e A343656 1 11 10 17 8 49 6 13 7 9 2 1
%e A343656 1 12 11 19 9 64 7 16 9 16 3 6 1
%e A343656 1 13 12 21 10 81 8 19 11 25 4 15 2 1
%e A343656 For example, row n = 8 counts the following divisors:
%e A343656 1 64 243 256 125 36 7 1
%e A343656 32 81 128 25 18 1
%e A343656 16 27 64 5 12
%e A343656 8 9 32 1 9
%e A343656 4 3 16 6
%e A343656 2 1 8 4
%e A343656 1 4 3
%e A343656 2 2
%e A343656 1 1
%t A343656 Table[DivisorSigma[0,k^(n-k)],{n,10},{k,n}]
%o A343656 (PARI) A(n, k) = numdiv(n^k); \\ _Seiichi Manyama_, May 15 2021
%Y A343656 Columns k=1..9 of the array give A000005, A048691, A048785, A344327, A344328, A344329, A343526, A344335, A344336.
%Y A343656 Row n = 6 of the array is A000290.
%Y A343656 Diagonal n = k of the array is A062319.
%Y A343656 Array antidiagonal sums (row sums of the triangle) are A343657.
%Y A343656 Dominated by A343658.
%Y A343656 A000312 = n^n.
%Y A343656 A007318 counts k-sets of elements of {1..n}.
%Y A343656 A009998(n,k) = n^k (as an array, offset 1).
%Y A343656 A059481 counts k-multisets of elements of {1..n}.
%Y A343656 Cf. A000169, A000272, A002064, A002109, A066959, A143773, A146291, A176029, A251683, A282935, A326358, A327527, A334996, A343652.
%K A343656 nonn,tabl
%O A343656 1,5
%A A343656 _Gus Wiseman_, Apr 28 2021