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A337485
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Number of pairwise coprime integer partitions of n with no 1's, where a singleton is not considered coprime unless it is (1).
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29
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0, 0, 0, 0, 0, 1, 0, 2, 1, 2, 2, 4, 3, 5, 4, 4, 7, 8, 9, 10, 10, 9, 13, 17, 18, 17, 19, 19, 24, 29, 34, 33, 31, 31, 42, 42, 56, 55, 50, 54, 66, 77, 86, 86, 79, 81, 96, 124, 127, 126, 127, 126, 145, 181, 190, 184, 183, 192, 212, 262, 289, 278, 257, 270, 311
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OFFSET
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0,8
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COMMENTS
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Such a partition is necessarily strict.
The Heinz numbers of these partitions are the intersection of A005408 (no 1's), A005117 (strict), and A302696 (coprime).
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LINKS
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FORMULA
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EXAMPLE
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The a(n) partitions for n = 5, 7, 12, 13, 16, 17, 18, 19 (A..H = 10..17):
(3,2) (4,3) (7,5) (7,6) (9,7) (9,8) (B,7) (A,9)
(5,2) (5,4,3) (8,5) (B,5) (A,7) (D,5) (B,8)
(7,3,2) (9,4) (D,3) (B,6) (7,6,5) (C,7)
(A,3) (7,5,4) (C,5) (8,7,3) (D,6)
(B,2) (8,5,3) (D,4) (9,5,4) (E,5)
(9,5,2) (E,3) (9,7,2) (F,4)
(B,3,2) (F,2) (B,4,3) (G,3)
(7,5,3,2) (B,5,2) (H,2)
(D,3,2) (B,5,3)
(7,5,4,3)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], !MemberQ[#, 1]&&CoprimeQ@@#&]], {n, 0, 30}]
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CROSSREFS
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A007359 considers all singletons to be coprime.
A337452 is the relatively prime instead of pairwise coprime version, with non-strict version A302698.
A337563 is the restriction to partitions of length 3.
A002865 counts partitions with no 1's.
A078374 counts relatively prime strict partitions.
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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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