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 A308558 #5 Jun 08 2019 17:55:06
%S A308558 1,1,2,1,2,2,1,4,2,2,1,4,2,2,2,1,6,3,2,2,2,1,6,3,2,2,2,2,1,10,3,3,2,2,
%T A308558 2,2,1,10,5,3,2,2,2,2,2,1,14,5,3,3,2,2,2,2,2,1,14,5,3,3,2,2,2,2,2,2,1,
%U A308558 20,7,4,3,3,2,2,2,2,2,2,1,20,7,4,3,3,2
%N A308558 Triangle read by rows where T(n,k) is the number of integer partitions of n > 0 into powers of k > 0.
%e A308558 Triangle begins:
%e A308558 1
%e A308558 1 2
%e A308558 1 2 2
%e A308558 1 4 2 2
%e A308558 1 4 2 2 2
%e A308558 1 6 3 2 2 2
%e A308558 1 6 3 2 2 2 2
%e A308558 1 10 3 3 2 2 2 2
%e A308558 1 10 5 3 2 2 2 2 2
%e A308558 1 14 5 3 3 2 2 2 2 2
%e A308558 1 14 5 3 3 2 2 2 2 2 2
%e A308558 1 20 7 4 3 3 2 2 2 2 2 2
%e A308558 1 20 7 4 3 3 2 2 2 2 2 2 2
%e A308558 Row n = 6 counts the following partitions:
%e A308558 (111111) (42) (33) (411) (51) (6)
%e A308558 (222) (3111) (111111) (111111) (111111)
%e A308558 (411) (111111)
%e A308558 (2211)
%e A308558 (21111)
%e A308558 (111111)
%t A308558 Table[If[k==1,1,Length[Select[IntegerPartitions[n],And@@(IntegerQ[Log[k,#]]&/@#)&]]],{n,10},{k,n}]
%Y A308558 Same as A102430 except for the k = 1 column.
%Y A308558 Row sums are A102431(n) + 1.
%Y A308558 Column k = 2 is A018819.
%Y A308558 Column k = 3 is A062051.
%Y A308558 Cf. A000961, A001597, A007916, A008284, A023894, A052410, A101417, A112344, A323053, A323054.
%K A308558 nonn,tabl
%O A308558 1,3
%A A308558 _Gus Wiseman_, Jun 07 2019