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 A328220 #8 Dec 26 2020 03:31:10
%S A328220 1,1,1,1,1,1,2,1,2,2,3,1,5,1,5,4,6,3,10,3,11,7,12,3,19,5,18,12,23,9,
%T A328220 36,11,33,21,40,20,58,19,58,35,70,31,98,36,101,65,112,56,155,64,164,
%U A328220 97,188,88,250,112,256,157,293,145,392,163,399,241,461,242
%N A328220 Number of strict integer partitions of n with no pair of consecutive parts relatively prime.
%H A328220 Fausto A. C. Cariboni, <a href="/A328220/b328220.txt">Table of n, a(n) for n = 0..500</a>
%e A328220 The a(2) = 1 through a(20) = 11 partitions (A..K = 10..20):
%e A328220 2 3 4 5 6 7 8 9 A B C D E F G H I J K
%e A328220 42 62 63 64 84 86 96 A6 863 A8 964 C8
%e A328220 82 93 A4 A5 C4 962 C6 A63 E6
%e A328220 A2 C2 C3 E2 E4 F5
%e A328220 642 842 862 F3 G4
%e A328220 A42 G2 I2
%e A328220 864 A64
%e A328220 963 A82
%e A328220 A62 C62
%e A328220 C42 E42
%e A328220 8642
%t A328220 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&!MatchQ[#,{___,x_,y_,___}/;GCD[x,y]==1]&]],{n,0,30}]
%Y A328220 The non-strict case is A328187.
%Y A328220 Partitions with all consecutive parts relatively prime are A328172, with strict case A328188.
%Y A328220 Strict partitions with relatively prime parts are A078374.
%Y A328220 Partitions with no consecutive divisibilities are A328171.
%Y A328220 Cf. A000837, A018783, A070211, A289509, A318980, A325545, A328170, A328221, A328335, A328336.
%K A328220 nonn
%O A328220 0,7
%A A328220 _Gus Wiseman_, Oct 14 2019