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 A328508 #8 Oct 19 2019 14:45:38
%S A328508 1,1,1,1,1,3,1,6,4,8,14,14,27,30,55,69,97,155,200,312,421,630,893,
%T A328508 1260,1864,2600,3813,5395,7801,11196,15971,23126,32917,47514,67993,
%U A328508 97670,140334,200913,289147,414119,595109,853751,1225086,1759405,2523151,3623984,5198759
%N A328508 Number of compositions of n with no part divisible by the next or the prior.
%H A328508 Andrew Howroyd, <a href="/A328508/b328508.txt">Table of n, a(n) for n = 0..1000</a>
%e A328508 The a(1) = 1 through a(11) = 14 compositions (A = 10, B = 11):
%e A328508 (1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B)
%e A328508 (23) (25) (35) (27) (37) (29)
%e A328508 (32) (34) (53) (45) (46) (38)
%e A328508 (43) (323) (54) (64) (47)
%e A328508 (52) (72) (73) (56)
%e A328508 (232) (234) (235) (65)
%e A328508 (252) (253) (74)
%e A328508 (432) (325) (83)
%e A328508 (343) (92)
%e A328508 (352) (254)
%e A328508 (523) (272)
%e A328508 (532) (353)
%e A328508 (2323) (434)
%e A328508 (3232) (452)
%t A328508 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],!MatchQ[#,{___,x_,y_,___}/;Divisible[y,x]||Divisible[x,y]]&]],{n,0,10}]
%o A328508 (PARI) seq(n)={my(r=matid(n)); for(k=1, n, for(i=1, k-1, r[i,k]=sum(j=1, k-i, if(i%j && j%i, r[j, k-i])))); concat([1], vecsum(Col(r)))} \\ _Andrew Howroyd_, Oct 19 2019
%Y A328508 The case of partitions is A328171.
%Y A328508 If we only forbid parts to be divisible by the next, we get A328460.
%Y A328508 Compositions with each part relatively prime to the next are A167606.
%Y A328508 Compositions with no part relatively prime to the next are A178470.
%Y A328508 Cf. A328026, A328028, A328161, A328172, A328189.
%K A328508 nonn
%O A328508 0,6
%A A328508 _Gus Wiseman_, Oct 17 2019
%E A328508 Terms a(26) and beyond from _Andrew Howroyd_, Oct 19 2019