cp's OEIS Frontend

A337462 Number of pairwise coprime compositions of n, where a singleton is not considered coprime unless it is (1).

%I A337462 #10 Feb 03 2021 23:10:29
%S A337462 1,1,1,3,6,12,21,37,62,100,159,253,402,634,983,1491,2224,3280,4813,
%T A337462 7043,10270,14888,21415,30585,43400,61204,85747,119295,164834,226422,
%U A337462 309663,422301,574826,781236,1060181,1436367,1942588,2622078,3531151,4742315,6348410
%N A337462 Number of pairwise coprime compositions of n, where a singleton is not considered coprime unless it is (1).
%C A337462 A composition of n is a finite sequence of positive integers summing to n.
%H A337462 Fausto A. C. Cariboni, <a href="/A337462/b337462.txt">Table of n, a(n) for n = 0..500</a>
%F A337462 For n > 1, a(n) = A101268(n) - 1.
%e A337462 The a(1) = 1 through a(5) = 12 compositions:
%e A337462   (1)  (1,1)  (1,2)    (1,3)      (1,4)
%e A337462               (2,1)    (3,1)      (2,3)
%e A337462               (1,1,1)  (1,1,2)    (3,2)
%e A337462                        (1,2,1)    (4,1)
%e A337462                        (2,1,1)    (1,1,3)
%e A337462                        (1,1,1,1)  (1,3,1)
%e A337462                                   (3,1,1)
%e A337462                                   (1,1,1,2)
%e A337462                                   (1,1,2,1)
%e A337462                                   (1,2,1,1)
%e A337462                                   (2,1,1,1)
%e A337462                                   (1,1,1,1,1)
%t A337462 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],#=={}||CoprimeQ@@#&]],{n,0,10}]
%Y A337462 A000740 counts the relatively prime instead of pairwise coprime version.
%Y A337462 A101268 considers all singletons to be coprime, with strict case A337562.
%Y A337462 A327516 is the unordered version.
%Y A337462 A333227 ranks these compositions, with complement A335239.
%Y A337462 A337461 counts these compositions of length 3.
%Y A337462 A337561 is the strict case.
%Y A337462 A051424 counts pairwise coprime or singleton partitions.
%Y A337462 A101268 counts pairwise coprime or singleton compositions.
%Y A337462 A178472 counts compositions with a common factor.
%Y A337462 A305713 counts strict pairwise coprime partitions.
%Y A337462 A328673 counts pairwise non-coprime partitions.
%Y A337462 A333228 ranks compositions whose distinct parts are pairwise coprime.
%Y A337462 A337667 counts pairwise non-coprime compositions.
%Y A337462 Cf. A001523, A007360, A087087, A220377, A302569, A307719, A326675, A335235, A335238, A337664.
%K A337462 nonn
%O A337462 0,4
%A A337462 _Gus Wiseman_, Sep 18 2020