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 A318729 Number of cyclic compositions (necklaces of positive integers) summing to n that have only one part or whose consecutive parts (including the last with first) are indivisible. 13
 1, 1, 1, 1, 2, 1, 3, 2, 4, 6, 6, 8, 11, 19, 21, 30, 41, 59, 79, 112, 157, 219, 305, 430, 605, 860, 1210, 1727, 2424, 3463, 4905, 7001, 9954, 14211, 20271, 28980, 41392, 59254, 84800, 121540, 174163, 249932, 358578, 515091, 739933, 1063827, 1529767, 2201383 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..100 FORMULA a(n) = A328600(n) + 1. - Andrew Howroyd, Oct 27 2019 EXAMPLE The a(13) = 11 cyclic compositions with successive parts indivisible:   (13)   (2,11) (3,10) (4,9) (5,8) (6,7)   (2,4,7) (2,6,5) (2,8,3) (3,6,4)   (2,3,5,3) MATHEMATICA neckQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And]; Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], Or[Length[#]==1, neckQ[#]&&And@@Not/@Divisible@@@Partition[#, 2, 1, 1]]&]], {n, 20}] PROG (PARI) 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, ]} seq(n)={my(v=sum(k=1, n, k*b(n, k, (i, j)->i%j<>0))); vector(n, n, 1 + sumdiv(n, d, eulerphi(d)*v[n/d])/n)} \\ Andrew Howroyd, Oct 27 2019 CROSSREFS Cf. A000740, A008965, A059966, A167606, A285573, A303362, A304713, A316476, A318726, A318727, A318728, A318730, A328600. Sequence in context: A117194 A340647 A318746 * A024467 A215489 A182167 Adjacent sequences:  A318726 A318727 A318728 * A318730 A318731 A318732 KEYWORD nonn AUTHOR Gus Wiseman, Sep 02 2018 EXTENSIONS Terms a(21) and beyond from Andrew Howroyd, Sep 08 2018 Name corrected by Gus Wiseman, Nov 04 2019 STATUS approved

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Last modified September 21 12:54 EDT 2021. Contains 347598 sequences. (Running on oeis4.)