cp's OEIS Frontend

A337983 Number of compositions of n into distinct parts, any two of which have a common divisor > 1.

%I A337983 #10 Oct 13 2020 14:34:46
%S A337983 1,0,1,1,1,1,3,1,3,3,5,1,13,1,13,7,19,1,35,1,59,15,65,1,117,5,133,27,
%T A337983 195,1,411,7,435,67,617,17,941,7,1177,135,1571,13,2939,31,3299,375,
%U A337983 4757,13,6709,43,8813,643,11307,61,16427,123,24331,1203,30461,67
%N A337983 Number of compositions of n into distinct parts, any two of which have a common divisor > 1.
%C A337983 Number of pairwise non-coprime strict compositions of n.
%e A337983 The a(2) = 1 through a(15) = 7 compositions (A..F = 10..15):
%e A337983   2  3  4  5  6   7  8   9   A   B  C    D  E    F
%e A337983               24     26  36  28     2A      2C   3C
%e A337983               42     62  63  46     39      4A   5A
%e A337983                              64     48      68   69
%e A337983                              82     84      86   96
%e A337983                                     93      A4   A5
%e A337983                                     A2      C2   C3
%e A337983                                     246     248
%e A337983                                     264     284
%e A337983                                     426     428
%e A337983                                     462     482
%e A337983                                     624     824
%e A337983                                     642     842
%t A337983 stabQ[u_,Q_]:=And@@Not/@Q@@@Tuples[u,2];
%t A337983 Table[Length[Join@@Permutations/@Select[IntegerPartitions[n],UnsameQ@@#&&stabQ[#,CoprimeQ]&]],{n,0,30}]
%Y A337983 A318717 is the unordered version.
%Y A337983 A318719 is the version for Heinz numbers of partitions.
%Y A337983 A337561 is the pairwise coprime instead of pairwise non-coprime version, or A337562 if singletons are considered coprime.
%Y A337983 A337605*6 counts these compositions of length 3.
%Y A337983 A337667 is the non-strict version, ranked by A337666.
%Y A337983 A337696 ranks these compositions.
%Y A337983 A051185 and A305843 (covering) count pairwise intersecting set-systems.
%Y A337983 A101268 counts pairwise coprime or singleton compositions.
%Y A337983 A200976 and A328673 are the unordered version.
%Y A337983 A233564 ranks strict compositions.
%Y A337983 A318749 is the version for factorizations, with non-strict version A319786.
%Y A337983 A333228 ranks compositions whose distinct parts are pairwise coprime.
%Y A337983 A335236 ranks compositions neither a singleton nor pairwise coprime.
%Y A337983 A337462 counts pairwise coprime compositions.
%Y A337983 A337694 lists numbers with no two relatively prime prime indices.
%Y A337983 Cf. A082024, A284825, A302797, A305713, A319752, A327516, A333227, A335235, A336737, A337604.
%K A337983 nonn
%O A337983 0,7
%A A337983 _Gus Wiseman_, Oct 06 2020