

A337485


Number of pairwise coprime integer partitions of n with no 1's, where a singleton is not considered coprime unless it is (1).


29



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

0,8


COMMENTS

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).


LINKS



FORMULA



EXAMPLE

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)


MATHEMATICA

Table[Length[Select[IntegerPartitions[n], !MemberQ[#, 1]&&CoprimeQ@@#&]], {n, 0, 30}]


CROSSREFS

A007359 considers all singletons to be coprime.
A337452 is the relatively prime instead of pairwise coprime version, with nonstrict version A302698.
A337563 is the restriction to partitions of length 3.
A002865 counts partitions with no 1's.
A078374 counts relatively prime strict partitions.


KEYWORD

nonn


AUTHOR



STATUS

approved



