A101268 Number of compositions of n into pairwise relatively prime parts.

1, 1, 2, 4, 7, 13, 22, 38, 63, 101, 160, 254, 403, 635, 984, 1492, 2225, 3281, 4814, 7044, 10271, 14889, 21416, 30586, 43401, 61205, 85748, 119296, 164835, 226423, 309664, 422302, 574827, 781237, 1060182, 1436368, 1942589, 2622079, 3531152, 4742316, 6348411

Offset: 0

Author

Vladeta Jovovic, Dec 18 2004

Keywords

• nonn

Comments

Here a singleton is always considered pairwise relatively prime. Compare to A337462. - Gus Wiseman, Oct 18 2020

Examples

			From _Gus Wiseman_, Oct 18 2020: (Start)
The a(1) = 1 through a(5) = 13 compositions:
  (1)  (2)   (3)    (4)     (5)
       (11)  (12)   (13)    (14)
             (21)   (31)    (23)
             (111)  (112)   (32)
                    (121)   (41)
                    (211)   (113)
                    (1111)  (131)
                            (311)
                            (1112)
                            (1121)
                            (1211)
                            (2111)
                            (11111)
(End)
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..500 (terms 0..400 from Alois P. Heinz)
• Temba Shonhiwa, Compositions with pairwise relatively prime summands within a restricted setting, Fibonacci Quart. 44 (2006), no. 4, 316-323.

Crossrefs

Row sums of A282748.

A051424 is the unordered version, with strict case A007360.

A335235 ranks these compositions.

A337461 counts these compositions of length 3, with unordered version A307719 and unordered strict version A220377.

A337462 does not consider a singleton to be coprime unless it is (1), with strict version A337561.

A337562 is the strict case.

A337664 looks only at distinct parts, with non-constant version A337665.

A000740 counts relatively prime compositions, with strict case A332004.

A178472 counts compositions with a common factor.

Cf. A087087, A302569, A305713, A326675, A327516, A328673, A333227, A333228.

Programs

Mathematica

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],Length[#]<=1||CoprimeQ@@#&]],{n,0,10}] (* Gus Wiseman, Oct 18 2020 *)

Formula

It seems that no formula is known.

Extensions

a(0)=1 prepended by Alois P. Heinz, Jun 14 2017