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A337450
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Number of relatively prime compositions of n with no 1's.
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11
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0, 0, 0, 0, 0, 2, 0, 7, 5, 17, 17, 54, 51, 143, 168, 358, 482, 986, 1313, 2583, 3663, 6698, 9921, 17710, 26489, 46352, 70928, 121137, 188220, 317810, 497322, 832039, 1313501, 2177282, 3459041, 5702808, 9094377, 14930351, 23895672, 39084070, 62721578
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OFFSET
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0,6
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COMMENTS
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A composition of n is a finite sequence of positive integers summing to n.
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LINKS
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EXAMPLE
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The a(5) = 2 through a(10) = 17 compositions (empty column indicated by dot):
(2,3) . (2,5) (3,5) (2,7) (3,7)
(3,2) (3,4) (5,3) (4,5) (7,3)
(4,3) (2,3,3) (5,4) (2,3,5)
(5,2) (3,2,3) (7,2) (2,5,3)
(2,2,3) (3,3,2) (2,2,5) (3,2,5)
(2,3,2) (2,3,4) (3,3,4)
(3,2,2) (2,4,3) (3,4,3)
(2,5,2) (3,5,2)
(3,2,4) (4,3,3)
(3,4,2) (5,2,3)
(4,2,3) (5,3,2)
(4,3,2) (2,2,3,3)
(5,2,2) (2,3,2,3)
(2,2,2,3) (2,3,3,2)
(2,2,3,2) (3,2,2,3)
(2,3,2,2) (3,2,3,2)
(3,2,2,2) (3,3,2,2)
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MAPLE
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b:= proc(n, g) option remember; `if`(n=0,
`if`(g=1, 1, 0), add(b(n-j, igcd(g, j)), j=2..n))
end:
a:= n-> b(n, 0):
seq(a(n), n=0..42);
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MATHEMATICA
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Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], !MemberQ[#, 1]&&GCD@@#==1&]], {n, 0, 15}]
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CROSSREFS
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A000740 is the version allowing 1's.
2*A055684(n) is the case of length 2.
A337452 is the unordered strict version.
A000837 counts relatively prime partitions.
A002865 counts partitions with no 1's.
A101268 counts singleton or pairwise coprime compositions.
A212804 counts compositions with no 1's.
A291166 appears to rank relatively prime compositions.
A337462 counts pairwise coprime compositions.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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