cp's OEIS Frontend

A337485 Number of pairwise coprime integer partitions of n with no 1's, where a singleton is not considered coprime unless it is (1).

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