cp's OEIS Frontend

A337667 Number of compositions of n where any two parts have a common divisor > 1.

%I A337667 #13 Feb 09 2021 18:38:31
%S A337667 1,0,1,1,2,1,5,1,8,4,17,1,38,1,65,19,128,1,284,1,518,67,1025,1,2168,
%T A337667 16,4097,256,8198,1,16907,7,32768,1027,65537,79,133088,19,262145,4099,
%U A337667 524408,25,1056731,51,2097158,16636,4194317,79,8421248,196,16777712
%N A337667 Number of compositions of n where any two parts have a common divisor > 1.
%C A337667 First differs from A178472 at a(31) = 7, a(31) = 1.
%H A337667 Fausto A. C. Cariboni, <a href="/A337667/b337667.txt">Table of n, a(n) for n = 0..290</a>
%e A337667 The a(2) = 1 through a(10) = 17 compositions (A = 10):
%e A337667    2   3   4    5   6     7   8      9     A
%e A337667            22       24        26     36    28
%e A337667                     33        44     63    46
%e A337667                     42        62     333   55
%e A337667                     222       224          64
%e A337667                               242          82
%e A337667                               422          226
%e A337667                               2222         244
%e A337667                                            262
%e A337667                                            424
%e A337667                                            442
%e A337667                                            622
%e A337667                                            2224
%e A337667                                            2242
%e A337667                                            2422
%e A337667                                            4222
%e A337667                                            22222
%t A337667 stabQ[u_,Q_]:=And@@Not/@Q@@@Tuples[u,2];
%t A337667 Table[Length[Join@@Permutations/@Select[IntegerPartitions[n],stabQ[#,CoprimeQ]&]],{n,0,15}]
%Y A337667 A101268 = 1 + A337462 is the pairwise coprime version.
%Y A337667 A328673 = A200976 + 1 is the unordered version.
%Y A337667 A337604 counts these compositions of length 3.
%Y A337667 A337666 ranks these compositions.
%Y A337667 A337694 gives Heinz numbers of the unordered version.
%Y A337667 A337983 is the strict case.
%Y A337667 A051185 counts intersecting set-systems, with spanning case A305843.
%Y A337667 A318717 is the unordered strict case.
%Y A337667 A319786 is the version for factorizations, with strict case A318749.
%Y A337667 A327516 counts pairwise coprime partitions.
%Y A337667 A333227 ranks pairwise coprime compositions.
%Y A337667 A333228 ranks compositions whose distinct parts are pairwise coprime.
%Y A337667 Cf. A051424, A082024, A178472, A284825, A319752, A327039, A337599, A337605, A337665.
%K A337667 nonn
%O A337667 0,5
%A A337667 _Gus Wiseman_, Oct 05 2020