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A337562 Number of pairwise coprime strict compositions of n, where a singleton is always considered coprime.

%I A337562 #11 Jan 19 2021 01:09:06
%S A337562 1,1,1,3,3,5,9,7,17,13,23,41,41,67,49,75,75,155,211,229,243,241,287,
%T A337562 395,807,537,841,655,1147,1619,2037,2551,2213,2007,2663,4579,4171,
%U A337562 7123,4843,6013,6215,11639,13561,16489,14739,15445,16529,25007,41003,32803
%N A337562 Number of pairwise coprime strict compositions of n, where a singleton is always considered coprime.
%H A337562 Fausto A. C. Cariboni, <a href="/A337562/b337562.txt">Table of n, a(n) for n = 0..600</a>
%F A337562 a(n > 1) = A337561(n) + 1 for n > 1.
%e A337562 The a(1) = 1 through a(9) = 12 compositions:
%e A337562   (1)  (2)  (3)    (4)    (5)    (6)      (7)    (8)      (9)
%e A337562             (1,2)  (1,3)  (1,4)  (1,5)    (1,6)  (1,7)    (1,8)
%e A337562             (2,1)  (3,1)  (2,3)  (5,1)    (2,5)  (3,5)    (2,7)
%e A337562                           (3,2)  (1,2,3)  (3,4)  (5,3)    (4,5)
%e A337562                           (4,1)  (1,3,2)  (4,3)  (7,1)    (5,4)
%e A337562                                  (2,1,3)  (5,2)  (1,2,5)  (7,2)
%e A337562                                  (2,3,1)  (6,1)  (1,3,4)  (8,1)
%e A337562                                  (3,1,2)         (1,4,3)  (1,3,5)
%e A337562                                  (3,2,1)         (1,5,2)  (1,5,3)
%e A337562                                                  (2,1,5)  (3,1,5)
%e A337562                                                  (2,5,1)  (3,5,1)
%e A337562                                                  (3,1,4)  (5,1,3)
%e A337562                                                  (3,4,1)  (5,3,1)
%e A337562                                                  (4,1,3)
%e A337562                                                  (4,3,1)
%e A337562                                                  (5,1,2)
%e A337562                                                  (5,2,1)
%t A337562 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],UnsameQ@@#&&(Length[#]<=1||CoprimeQ@@#)&]],{n,0,10}]
%Y A337562 A007360 is the unordered version, with non-strict version A051424.
%Y A337562 A101268 is the not necessarily strict version.
%Y A337562 A220377*6 counts these compositions of length 3.
%Y A337562 A337561 does not consider a singleton to be coprime unless it is (1), with non-strict version A337462.
%Y A337562 A337664 looks only at distinct parts.
%Y A337562 A000740 counts relatively prime compositions, with strict case A332004.
%Y A337562 A072706 counts unimodal strict compositions.
%Y A337562 A178472 counts compositions with a common factor.
%Y A337562 A327516 counts pairwise coprime partitions, with strict case A305713.
%Y A337562 A328673 counts pairwise non-coprime partitions.
%Y A337562 A333228 ranks compositions whose distinct parts are pairwise coprime.
%Y A337562 Cf. A087087, A220377, A302569, A307719, A326675, A333227, A335235, A335238, A337461, A337665.
%K A337562 nonn
%O A337562 0,4
%A A337562 _Gus Wiseman_, Sep 20 2020