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%I #26 Feb 03 2021 23:10:21
%S 1,1,2,4,7,13,22,38,63,101,160,254,403,635,984,1492,2225,3281,4814,
%T 7044,10271,14889,21416,30586,43401,61205,85748,119296,164835,226423,
%U 309664,422302,574827,781237,1060182,1436368,1942589,2622079,3531152,4742316,6348411
%N Number of compositions of n into pairwise relatively prime parts.
%C Here a singleton is always considered pairwise relatively prime. Compare to A337462. - _Gus Wiseman_, Oct 18 2020
%H Fausto A. C. Cariboni, <a href="/A101268/b101268.txt">Table of n, a(n) for n = 0..500</a> (terms 0..400 from Alois P. Heinz)
%H Temba Shonhiwa, <a href="http://www.fq.math.ca/Papers1/44-4/quarttemba04_2006.pdf">Compositions with pairwise relatively prime summands within a restricted setting</a>, Fibonacci Quart. 44 (2006), no. 4, 316-323.
%F It seems that no formula is known.
%e From _Gus Wiseman_, Oct 18 2020: (Start)
%e The a(1) = 1 through a(5) = 13 compositions:
%e (1) (2) (3) (4) (5)
%e (11) (12) (13) (14)
%e (21) (31) (23)
%e (111) (112) (32)
%e (121) (41)
%e (211) (113)
%e (1111) (131)
%e (311)
%e (1112)
%e (1121)
%e (1211)
%e (2111)
%e (11111)
%e (End)
%t Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],Length[#]<=1||CoprimeQ@@#&]],{n,0,10}] (* _Gus Wiseman_, Oct 18 2020 *)
%Y Row sums of A282748.
%Y A051424 is the unordered version, with strict case A007360.
%Y A335235 ranks these compositions.
%Y A337461 counts these compositions of length 3, with unordered version A307719 and unordered strict version A220377.
%Y A337462 does not consider a singleton to be coprime unless it is (1), with strict version A337561.
%Y A337562 is the strict case.
%Y A337664 looks only at distinct parts, with non-constant version A337665.
%Y A000740 counts relatively prime compositions, with strict case A332004.
%Y A178472 counts compositions with a common factor.
%Y Cf. A087087, A302569, A305713, A326675, A327516, A328673, A333227, A333228.
%K nonn
%O 0,3
%A _Vladeta Jovovic_, Dec 18 2004
%E a(0)=1 prepended by _Alois P. Heinz_, Jun 14 2017
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