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 A328598 #10 Oct 27 2019 04:58:26
%S A328598 1,0,0,0,0,2,0,4,2,7,12,11,22,26,55,63,99,149,215,324,458,699,1006,
%T A328598 1492,2185,3202,4734,6928,10242,14951,22023,32365,47557,69905,102633,
%U A328598 150983,221712,325918,478841,703647,1034103,1519431,2233061,3281003,4821790,7085358
%N A328598 Number of compositions of n with no part circularly followed by a divisor.
%C A328598 A composition of n is a finite sequence of positive integers summing to n.
%C A328598 Circularity means the last part is followed by the first.
%H A328598 Andrew Howroyd, <a href="/A328598/b328598.txt">Table of n, a(n) for n = 0..200</a>
%F A328598 a(n > 0) = A318726(n) - 1.
%e A328598 The a(5) = 2 through a(12) = 22 compositions (empty column not shown):
%e A328598 (2,3) (2,5) (3,5) (2,7) (3,7) (2,9) (5,7)
%e A328598 (3,2) (3,4) (5,3) (4,5) (4,6) (3,8) (7,5)
%e A328598 (4,3) (5,4) (6,4) (4,7) (2,3,7)
%e A328598 (5,2) (7,2) (7,3) (5,6) (2,7,3)
%e A328598 (2,4,3) (2,3,5) (6,5) (3,2,7)
%e A328598 (3,2,4) (2,5,3) (7,4) (3,4,5)
%e A328598 (4,3,2) (3,2,5) (8,3) (3,5,4)
%e A328598 (3,5,2) (9,2) (3,7,2)
%e A328598 (5,2,3) (2,4,5) (4,3,5)
%e A328598 (5,3,2) (4,5,2) (4,5,3)
%e A328598 (2,3,2,3) (5,2,4) (5,3,4)
%e A328598 (3,2,3,2) (5,4,3)
%e A328598 (7,2,3)
%e A328598 (7,3,2)
%e A328598 (2,3,2,5)
%e A328598 (2,3,4,3)
%e A328598 (2,5,2,3)
%e A328598 (3,2,3,4)
%e A328598 (3,2,5,2)
%e A328598 (3,4,3,2)
%e A328598 (4,3,2,3)
%e A328598 (5,2,3,2)
%t A328598 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],And@@Not/@Divisible@@@Partition[#,2,1,1]&]],{n,0,10}]
%o A328598 (PARI)
%o A328598 b(n, q, pred)={my(M=matrix(n, n)); for(k=1, n, M[k, k]=pred(q, k); for(i=1, k-1, M[i, k]=sum(j=1, k-i, if(pred(j, i), M[j, k-i], 0)))); M[q,]}
%o A328598 seq(n)={concat([1], sum(k=1, n, b(n, k, (i,j)->i%j<>0)))} \\ _Andrew Howroyd_, Oct 26 2019
%Y A328598 The necklace version is A328600, or A318729 without singletons.
%Y A328598 The version with singletons is A318726.
%Y A328598 The non-circular version is A328460.
%Y A328598 Also forbidding parts circularly followed by a multiple gives A328599.
%Y A328598 Partitions with no part followed by a divisor are A328171.
%Y A328598 Cf. A000740, A008965, A167606, A178470, A318748, A328187, A328508, A328593, A328597, A328601, A328603, A328609.
%K A328598 nonn
%O A328598 0,6
%A A328598 _Gus Wiseman_, Oct 24 2019
%E A328598 Terms a(26) and beyond from _Andrew Howroyd_, Oct 26 2019