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 A328460 #7 Oct 19 2019 14:45:07
%S A328460 1,1,1,2,2,4,5,8,11,16,26,35,53,76,115,168,244,363,528,782,1144,1685,
%T A328460 2474,3633,5347,7844,11539,16946,24919,36605,53782,79053,116142,
%U A328460 170700,250800,368585,541610,795884,1169572,1718593,2525522,3711134,5453542,8013798,11776138
%N A328460 Number of compositions of n with no part divisible by the next.
%H A328460 Andrew Howroyd, <a href="/A328460/b328460.txt">Table of n, a(n) for n = 0..1000</a>
%e A328460 The a(1) = 1 through a(9) = 16 compositions:
%e A328460 (1) (2) (3) (4) (5) (6) (7) (8) (9)
%e A328460 (21) (31) (23) (42) (25) (35) (27)
%e A328460 (32) (51) (34) (53) (45)
%e A328460 (41) (231) (43) (62) (54)
%e A328460 (321) (52) (71) (63)
%e A328460 (61) (251) (72)
%e A328460 (232) (323) (81)
%e A328460 (421) (341) (234)
%e A328460 (431) (252)
%e A328460 (521) (342)
%e A328460 (2321) (351)
%e A328460 (423)
%e A328460 (432)
%e A328460 (531)
%e A328460 (621)
%e A328460 (3231)
%t A328460 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],!MatchQ[#,{___,x_,y_,___}/;Divisible[y,x]]&]],{n,0,10}]
%o A328460 (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(j%i, r[j, k-i])))); concat([1], vecsum(Col(r)))} \\ _Andrew Howroyd_, Oct 19 2019
%Y A328460 The case of partitions is A328171.
%Y A328460 If we also require no part to be divisible by the prior, we get A328508.
%Y A328460 Compositions with each part relatively prime to the next are A167606.
%Y A328460 Compositions with no part relatively prime to the next are A178470.
%Y A328460 Cf. A328026, A328028, A328161, A328172, A328189.
%K A328460 nonn
%O A328460 0,4
%A A328460 _Gus Wiseman_, Oct 17 2019
%E A328460 Terms a(26) and beyond from _Andrew Howroyd_, Oct 19 2019