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%I #15 Feb 14 2021 02:56:55
%S 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,
%T 29,34,33,31,31,42,42,56,55,50,54,66,77,86,86,79,81,96,124,127,126,
%U 127,126,145,181,190,184,183,192,212,262,289,278,257,270,311
%N Number of pairwise coprime integer partitions of n with no 1's, where a singleton is not considered coprime unless it is (1).
%C Such a partition is necessarily strict.
%C The Heinz numbers of these partitions are the intersection of A005408 (no 1's), A005117 (strict), and A302696 (coprime).
%H Fausto A. C. Cariboni, <a href="/A337485/b337485.txt">Table of n, a(n) for n = 0..750</a>
%F a(n) = A007359(n) - 1 for n > 1.
%e The a(n) partitions for n = 5, 7, 12, 13, 16, 17, 18, 19 (A..H = 10..17):
%e (3,2) (4,3) (7,5) (7,6) (9,7) (9,8) (B,7) (A,9)
%e (5,2) (5,4,3) (8,5) (B,5) (A,7) (D,5) (B,8)
%e (7,3,2) (9,4) (D,3) (B,6) (7,6,5) (C,7)
%e (A,3) (7,5,4) (C,5) (8,7,3) (D,6)
%e (B,2) (8,5,3) (D,4) (9,5,4) (E,5)
%e (9,5,2) (E,3) (9,7,2) (F,4)
%e (B,3,2) (F,2) (B,4,3) (G,3)
%e (7,5,3,2) (B,5,2) (H,2)
%e (D,3,2) (B,5,3)
%e (7,5,4,3)
%t Table[Length[Select[IntegerPartitions[n],!MemberQ[#,1]&&CoprimeQ@@#&]],{n,0,30}]
%Y A005408 intersected with A302696 ranks these partitions.
%Y A007359 considers all singletons to be coprime.
%Y A327516 allows 1's, with non-strict version A305713.
%Y A337452 is the relatively prime instead of pairwise coprime version, with non-strict version A302698.
%Y A337563 is the restriction to partitions of length 3.
%Y A002865 counts partitions with no 1's.
%Y A078374 counts relatively prime strict partitions.
%Y A200976 and A328673 count pairwise non-coprime partitions.
%Y Cf. A101268, A220377, A302696, A304709, A332004, A337450, A337451, A337462, A337561, A337605.
%K nonn
%O 0,8
%A _Gus Wiseman_, Sep 21 2020
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