cp's OEIS Frontend

A337697 Number of pairwise coprime compositions of n with no 1's, where a singleton is not considered coprime.

%I A337697 #11 Oct 13 2020 14:33:52
%S A337697 0,0,0,0,0,2,0,4,2,4,8,8,14,10,16,12,30,38,46,46,48,52,62,152,96,156,
%T A337697 112,190,256,338,420,394,326,402,734,622,1150,802,946,898,1730,1946,
%U A337697 2524,2200,2328,2308,3356,5816,4772,5350,4890,6282,6316,12092,8902
%N A337697 Number of pairwise coprime compositions of n with no 1's, where a singleton is not considered coprime.
%C A337697 A composition of n is a finite sequence of positive integers summing to n. These compositions must be strict.
%F A337697 For n > 1, the version where singletons are considered coprime is a(n) + 1.
%e A337697 The a(5) = 2 through a(12) = 14 compositions (empty column indicated by dot):
%e A337697   (2,3)  .  (2,5)  (3,5)  (2,7)  (3,7)    (2,9)  (5,7)
%e A337697   (3,2)     (3,4)  (5,3)  (4,5)  (7,3)    (3,8)  (7,5)
%e A337697             (4,3)         (5,4)  (2,3,5)  (4,7)  (2,3,7)
%e A337697             (5,2)         (7,2)  (2,5,3)  (5,6)  (2,7,3)
%e A337697                                  (3,2,5)  (6,5)  (3,2,7)
%e A337697                                  (3,5,2)  (7,4)  (3,4,5)
%e A337697                                  (5,2,3)  (8,3)  (3,5,4)
%e A337697                                  (5,3,2)  (9,2)  (3,7,2)
%e A337697                                                  (4,3,5)
%e A337697                                                  (4,5,3)
%e A337697                                                  (5,3,4)
%e A337697                                                  (5,4,3)
%e A337697                                                  (7,2,3)
%e A337697                                                  (7,3,2)
%t A337697 Table[Length[Join@@Permutations/@Select[IntegerPartitions[n],!MemberQ[#,1]&&CoprimeQ@@#&]],{n,0,30}]
%Y A337697 A022340 intersected with A333227 is a ranking sequence (using standard compositions A066099) for these compositions.
%Y A337697 A212804 does not require coprimality, with unordered version A002865.
%Y A337697 A337450 is the relatively prime instead of pairwise coprime version, with strict case A337451 and unordered version A302698.
%Y A337697 A337462 allows 1's, with strict case A337561 (or A101268 with singletons), unordered version A327516 with Heinz numbers A302696, and 3-part case A337461.
%Y A337697 A337485 is the unordered version (or A007359 with singletons considered coprime), with Heinz numbers A337984.
%Y A337697 A337563 is the case of unordered triples.
%Y A337697 Cf. A078374, A178472, A302568, A302697, A305713, A307719, A332004, A337562.
%K A337697 nonn
%O A337697 0,6
%A A337697 _Gus Wiseman_, Oct 06 2020