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 A338554 #10 Nov 09 2020 21:35:22
%S A338554 0,0,0,0,0,0,1,0,2,1,5,0,9,0,13,6,18,0,33,0,40,14,54,0,87,5,99,27,133,
%T A338554 0,211,0,226,55,295,18,443,0,488,100,637,0,912,0,1000,198,1253,0,1775,
%U A338554 13,1988,296,2434,0,3358,59,3728,489,4563,0,6241,0,6840,814
%N A338554 Number of non-constant integer partitions of n whose parts have a common divisor > 1.
%F A338554 For n > 0, a(n) = A018783(n) - A000005(n) + 1.
%e A338554 The a(6) = 2 through a(15) = 6 partitions (empty columns indicated by dots, A = 10, B = 11, C = 12):
%e A338554 (42) . (62) (63) (64) . (84) . (86) (96)
%e A338554 (422) (82) (93) (A4) (A5)
%e A338554 (442) (A2) (C2) (C3)
%e A338554 (622) (633) (644) (663)
%e A338554 (4222) (642) (662) (933)
%e A338554 (822) (842) (6333)
%e A338554 (4422) (A22)
%e A338554 (6222) (4442)
%e A338554 (42222) (6422)
%e A338554 (8222)
%e A338554 (44222)
%e A338554 (62222)
%e A338554 (422222)
%t A338554 Table[Length[Select[IntegerPartitions[n],!SameQ@@#&&GCD@@#>1&]],{n,0,30}]
%Y A338554 A046022 lists positions of zeros.
%Y A338554 A082023(n) - A059841(n) is the 2-part version, n > 2.
%Y A338554 A303280(n) - 1 is the strict case (n > 1).
%Y A338554 A338552 lists the Heinz numbers of these partitions.
%Y A338554 A338553 counts the complement, with Heinz numbers A338555.
%Y A338554 A000005 counts constant partitions, with Heinz numbers A000961.
%Y A338554 A000837 counts relatively prime partitions, with Heinz numbers A289509.
%Y A338554 A018783 counts non-relatively prime partitions (ordered: A178472), with Heinz numbers A318978.
%Y A338554 A282750 counts relatively prime partitions by sum and length.
%Y A338554 Cf. A000010, A008284, A051424, A082024, A289508, A302698, A304712.
%K A338554 nonn
%O A338554 0,9
%A A338554 _Gus Wiseman_, Nov 07 2020