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A318715
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Number of strict integer partitions of n with relatively prime parts in which no two parts are relatively prime.
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19
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1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 1, 0, 4, 0, 3, 0, 1, 0, 5, 0, 8, 0, 2, 0, 5, 0, 10, 0, 4, 0, 13, 0, 15, 0, 3, 1, 13, 0, 19, 0, 9, 1, 24, 0, 20
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OFFSET
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1,41
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LINKS
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EXAMPLE
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The a(67) = 10 strict integer partitions are
(45,12,10) (42,15,10) (40,15,12) (33,22,12) (28,21,18)
(36,15,10,6) (30,15,12,10) (28,21,12,6) (24,18,15,10)
(24,15,12,10,6).
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], And[UnsameQ@@#, GCD@@#==1, And@@(GCD[##]>1&)@@@Select[Tuples[#, 2], Less@@#&]]&]], {n, 50}]
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CROSSREFS
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Cf. A007359, A051185, A078374, A303140, A303282, A303283, A305713, A305843, A305854, A318716, A318717, A318720.
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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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