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 A328187 #13 Dec 26 2020 16:06:54
%S A328187 1,1,1,1,2,1,4,1,5,3,8,1,14,1,16,9,22,3,38,4,46,19,58,9,94,18,106,41,
%T A328187 144,28,221,37,246,92,318,87,465,95,530,198,693,169,963,220,1108,424,
%U A328187 1383,381,1899,492,2216,815,2732,799,3644,1041,4231,1585,5194,1608
%N A328187 Number of integer partitions of n with no pair of consecutive parts relatively prime.
%H A328187 Fausto A. C. Cariboni, <a href="/A328187/b328187.txt">Table of n, a(n) for n = 0..300</a>
%e A328187 The a(1) = 1 through a(15) = 9 partitions (A..F = 10..15):
%e A328187 1 2 3 4 5 6 7 8 9 A B C D E F
%e A328187 22 33 44 63 55 66 77 96
%e A328187 42 62 333 64 84 86 A5
%e A328187 222 422 82 93 A4 C3
%e A328187 2222 442 A2 C2 555
%e A328187 622 444 644 663
%e A328187 4222 633 662 933
%e A328187 22222 642 842 6333
%e A328187 822 A22 33333
%e A328187 3333 4442
%e A328187 4422 6422
%e A328187 6222 8222
%e A328187 42222 44222
%e A328187 222222 62222
%e A328187 422222
%e A328187 2222222
%t A328187 Table[Length[Select[IntegerPartitions[n],!MatchQ[#,{___,x_,y_,___}/;GCD[x,y]==1]&]],{n,0,30}]
%Y A328187 The Heinz numbers of these partitions are given by A328336.
%Y A328187 The case of compositions is A178470.
%Y A328187 The strict case is A328220.
%Y A328187 Partitions with all pairs of consecutive parts relatively prime are A328172.
%Y A328187 Cf. A000837, A018783, A328028, A328170, A328171, A328188.
%K A328187 nonn
%O A328187 0,5
%A A328187 _Gus Wiseman_, Oct 12 2019