This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A332004 #13 Oct 21 2020 22:49:35
%S A332004 1,1,0,2,2,4,8,12,16,24,52,64,88,132,180,344,416,616,816,1176,1496,
%T A332004 2736,3232,4756,6176,8756,11172,15576,24120,30460,41456,55740,74440,
%U A332004 97976,130192,168408,256464,315972,429888,558192,749920,958264,1274928,1621272,2120288,3020256
%N A332004 Number of compositions (ordered partitions) of n into distinct and relatively prime parts.
%C A332004 Moebius transform of A032020.
%C A332004 Ranking these compositions using standard compositions (A066099) gives the intersection of A233564 (strict) with A291166 (relatively prime). - _Gus Wiseman_, Oct 18 2020
%H A332004 Alois P. Heinz, <a href="/A332004/b332004.txt">Table of n, a(n) for n = 0..10000</a>
%H A332004 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%e A332004 a(6) = 8 because we have [5, 1], [3, 2, 1], [3, 1, 2], [2, 3, 1], [2, 1, 3], [1, 5], [1, 3, 2] and [1, 2, 3].
%e A332004 From _Gus Wiseman_, Oct 18 2020: (Start)
%e A332004 The a(1) = 1 through a(8) = 16 compositions (empty column indicated by dot):
%e A332004 (1) . (1,2) (1,3) (1,4) (1,5) (1,6) (1,7)
%e A332004 (2,1) (3,1) (2,3) (5,1) (2,5) (3,5)
%e A332004 (3,2) (1,2,3) (3,4) (5,3)
%e A332004 (4,1) (1,3,2) (4,3) (7,1)
%e A332004 (2,1,3) (5,2) (1,2,5)
%e A332004 (2,3,1) (6,1) (1,3,4)
%e A332004 (3,1,2) (1,2,4) (1,4,3)
%e A332004 (3,2,1) (1,4,2) (1,5,2)
%e A332004 (2,1,4) (2,1,5)
%e A332004 (2,4,1) (2,5,1)
%e A332004 (4,1,2) (3,1,4)
%e A332004 (4,2,1) (3,4,1)
%e A332004 (4,1,3)
%e A332004 (4,3,1)
%e A332004 (5,1,2)
%e A332004 (5,2,1)
%e A332004 (End)
%t A332004 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],UnsameQ@@#&&GCD@@#<=1&]],{n,0,15}] (* _Gus Wiseman_, Oct 18 2020 *)
%Y A332004 Cf. A007360, A032020, A108700, A302698.
%Y A332004 A000740 is the non-strict version.
%Y A332004 A078374 is the unordered version (non-strict: A000837).
%Y A332004 A101271*6 counts these compositions of length 3 (non-strict: A000741).
%Y A332004 A337561/A337562 is the pairwise coprime instead of relatively prime version (non-strict: A337462/A101268).
%Y A332004 A289509 gives the Heinz numbers of relatively prime partitions.
%Y A332004 A333227/A335235 ranks pairwise coprime compositions.
%Y A332004 Cf. A001523, A178472, A216652, A289508, A291166, A333228.
%K A332004 nonn
%O A332004 0,4
%A A332004 _Ilya Gutkovskiy_, Feb 04 2020