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A337667
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Number of compositions of n where any two parts have a common divisor > 1.
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16
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1, 0, 1, 1, 2, 1, 5, 1, 8, 4, 17, 1, 38, 1, 65, 19, 128, 1, 284, 1, 518, 67, 1025, 1, 2168, 16, 4097, 256, 8198, 1, 16907, 7, 32768, 1027, 65537, 79, 133088, 19, 262145, 4099, 524408, 25, 1056731, 51, 2097158, 16636, 4194317, 79, 8421248, 196, 16777712
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OFFSET
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0,5
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COMMENTS
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First differs from A178472 at a(31) = 7, a(31) = 1.
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LINKS
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EXAMPLE
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The a(2) = 1 through a(10) = 17 compositions (A = 10):
2 3 4 5 6 7 8 9 A
22 24 26 36 28
33 44 63 46
42 62 333 55
222 224 64
242 82
422 226
2222 244
262
424
442
622
2224
2242
2422
4222
22222
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MATHEMATICA
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stabQ[u_, Q_]:=And@@Not/@Q@@@Tuples[u, 2];
Table[Length[Join@@Permutations/@Select[IntegerPartitions[n], stabQ[#, CoprimeQ]&]], {n, 0, 15}]
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CROSSREFS
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A337604 counts these compositions of length 3.
A337694 gives Heinz numbers of the unordered version.
A318717 is the unordered strict case.
A327516 counts pairwise coprime partitions.
A333227 ranks pairwise coprime compositions.
A333228 ranks compositions whose distinct parts are pairwise coprime.
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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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