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 A303138 #7 Apr 21 2018 20:57:48
%S A303138 1,0,1,1,0,1,1,0,0,1,2,0,0,0,1,2,1,0,0,0,1,4,0,0,0,0,0,1,4,1,0,0,0,0,
%T A303138 0,1,6,0,1,0,0,0,0,0,1,7,2,0,0,0,0,0,0,0,1,11,0,0,0,0,0,0,0,0,0,1,10,
%U A303138 2,1,1,0,0,0,0,0,0,0,1,17,0,0,0,0,0,0,0,0,0,0,0,1,17,4,0,0,0,0,0,0,0,0,0,0,0,1,23,0,2,0,1
%N A303138 Regular triangle where T(n,k) is the number of strict integer partitions of n with greatest common divisor k.
%F A303138 If k divides n, T(n,k) = A078374(n/k); otherwise T(n,k) = 0.
%e A303138 Triangle begins:
%e A303138 01: 1
%e A303138 02: 0 1
%e A303138 03: 1 0 1
%e A303138 04: 1 0 0 1
%e A303138 05: 2 0 0 0 1
%e A303138 06: 2 1 0 0 0 1
%e A303138 07: 4 0 0 0 0 0 1
%e A303138 08: 4 1 0 0 0 0 0 1
%e A303138 09: 6 0 1 0 0 0 0 0 1
%e A303138 10: 7 2 0 0 0 0 0 0 0 1
%e A303138 11: 11 0 0 0 0 0 0 0 0 0 1
%e A303138 12: 10 2 1 1 0 0 0 0 0 0 0 1
%e A303138 13: 17 0 0 0 0 0 0 0 0 0 0 0 1
%e A303138 14: 17 4 0 0 0 0 0 0 0 0 0 0 0 1
%e A303138 15: 23 0 2 0 1 0 0 0 0 0 0 0 0 0 1
%e A303138 The strict partitions counted in row 12 are the following.
%e A303138 T(12,1) = 10: (11,1) (9,2,1) (8,3,1) (7,5) (7,4,1) (7,3,2) (6,5,1) (6,3,2,1) (5,4,3) (5,4,2,1)
%e A303138 T(12,2) = 2: (10,2) (6,4,2)
%e A303138 T(12,3) = 1: (9,3)
%e A303138 T(12,4) = 1: (8,4)
%e A303138 T(12,12) = 1: (12)
%t A303138 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&GCD@@#===k&]],{n,15},{k,n}]
%Y A303138 First column is A078374. Second column at even indices is same as first column. Row sums are A000009. Row sums with first column removed are A303280.
%Y A303138 Cf. A000009, A000837, A018783, A051424, A117408, A168532, A289508, A289509, A298748, A300486, A302698, A302796, A303139, A303140, A303280.
%K A303138 nonn,tabl
%O A303138 1,11
%A A303138 _Gus Wiseman_, Apr 19 2018