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A328508
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Number of compositions of n with no part divisible by the next or the prior.
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10
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1, 1, 1, 1, 1, 3, 1, 6, 4, 8, 14, 14, 27, 30, 55, 69, 97, 155, 200, 312, 421, 630, 893, 1260, 1864, 2600, 3813, 5395, 7801, 11196, 15971, 23126, 32917, 47514, 67993, 97670, 140334, 200913, 289147, 414119, 595109, 853751, 1225086, 1759405, 2523151, 3623984, 5198759
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OFFSET
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0,6
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LINKS
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EXAMPLE
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The a(1) = 1 through a(11) = 14 compositions (A = 10, B = 11):
(1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B)
(23) (25) (35) (27) (37) (29)
(32) (34) (53) (45) (46) (38)
(43) (323) (54) (64) (47)
(52) (72) (73) (56)
(232) (234) (235) (65)
(252) (253) (74)
(432) (325) (83)
(343) (92)
(352) (254)
(523) (272)
(532) (353)
(2323) (434)
(3232) (452)
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MATHEMATICA
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Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], !MatchQ[#, {___, x_, y_, ___}/; Divisible[y, x]||Divisible[x, y]]&]], {n, 0, 10}]
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PROG
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(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
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CROSSREFS
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If we only forbid parts to be divisible by the next, we get A328460.
Compositions with each part relatively prime to the next are A167606.
Compositions with no part relatively prime to the next are A178470.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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