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 A328460 Number of compositions of n with no part divisible by the next. 14
 1, 1, 1, 2, 2, 4, 5, 8, 11, 16, 26, 35, 53, 76, 115, 168, 244, 363, 528, 782, 1144, 1685, 2474, 3633, 5347, 7844, 11539, 16946, 24919, 36605, 53782, 79053, 116142, 170700, 250800, 368585, 541610, 795884, 1169572, 1718593, 2525522, 3711134, 5453542, 8013798, 11776138 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..1000 EXAMPLE The a(1) = 1 through a(9) = 16 compositions:   (1)  (2)  (3)   (4)   (5)   (6)    (7)    (8)     (9)             (21)  (31)  (23)  (42)   (25)   (35)    (27)                         (32)  (51)   (34)   (53)    (45)                         (41)  (231)  (43)   (62)    (54)                               (321)  (52)   (71)    (63)                                      (61)   (251)   (72)                                      (232)  (323)   (81)                                      (421)  (341)   (234)                                             (431)   (252)                                             (521)   (342)                                             (2321)  (351)                                                     (423)                                                     (432)                                                     (531)                                                     (621)                                                     (3231) MATHEMATICA Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], !MatchQ[#, {___, x_, y_, ___}/; Divisible[y, x]]&]], {n, 0, 10}] PROG (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 CROSSREFS The case of partitions is A328171. If we also require no part to be divisible by the prior, we get A328508. Compositions with each part relatively prime to the next are A167606. Compositions with no part relatively prime to the next are A178470. Cf. A328026, A328028, A328161, A328172, A328189. Sequence in context: A089299 A017910 A240734 * A238478 A013979 A107458 Adjacent sequences:  A328457 A328458 A328459 * A328461 A328462 A328463 KEYWORD nonn AUTHOR Gus Wiseman, Oct 17 2019 EXTENSIONS Terms a(26) and beyond from Andrew Howroyd, Oct 19 2019 STATUS approved

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Last modified January 24 10:33 EST 2020. Contains 331193 sequences. (Running on oeis4.)