A337450 Number of relatively prime compositions of n with no 1's.

0, 0, 0, 0, 0, 2, 0, 7, 5, 17, 17, 54, 51, 143, 168, 358, 482, 986, 1313, 2583, 3663, 6698, 9921, 17710, 26489, 46352, 70928, 121137, 188220, 317810, 497322, 832039, 1313501, 2177282, 3459041, 5702808, 9094377, 14930351, 23895672, 39084070, 62721578

Offset: 0

Author

Gus Wiseman, Aug 31 2020

Keywords

• nonn

Comments

A composition of n is a finite sequence of positive integers summing to n.

Examples

			The a(5) = 2 through a(10) = 17 compositions (empty column indicated by dot):
  (2,3)  .  (2,5)    (3,5)    (2,7)      (3,7)
  (3,2)     (3,4)    (5,3)    (4,5)      (7,3)
            (4,3)    (2,3,3)  (5,4)      (2,3,5)
            (5,2)    (3,2,3)  (7,2)      (2,5,3)
            (2,2,3)  (3,3,2)  (2,2,5)    (3,2,5)
            (2,3,2)           (2,3,4)    (3,3,4)
            (3,2,2)           (2,4,3)    (3,4,3)
                              (2,5,2)    (3,5,2)
                              (3,2,4)    (4,3,3)
                              (3,4,2)    (5,2,3)
                              (4,2,3)    (5,3,2)
                              (4,3,2)    (2,2,3,3)
                              (5,2,2)    (2,3,2,3)
                              (2,2,2,3)  (2,3,3,2)
                              (2,2,3,2)  (3,2,2,3)
                              (2,3,2,2)  (3,2,3,2)
                              (3,2,2,2)  (3,3,2,2)
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000 (first 171 terms from Fausto A. C. Cariboni)

Crossrefs

A000740 is the version allowing 1's.

2*A055684(n) is the case of length 2.

A302697 ranks the unordered case.

A302698 is the unordered version.

A337451 is the strict version.

A337452 is the unordered strict version.

A000837 counts relatively prime partitions.

A002865 counts partitions with no 1's.

A101268 counts singleton or pairwise coprime compositions.

A212804 counts compositions with no 1's.

A291166 appears to rank relatively prime compositions.

A337462 counts pairwise coprime compositions.

Cf. A000010, A007359, A023023, A101268, A178472, A289509, A302568, A337485.

Programs

Maple

b:= proc(n, g) option remember; `if`(n=0,
     `if`(g=1, 1, 0), add(b(n-j, igcd(g, j)), j=2..n))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..42);

Mathematica

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],!MemberQ[#,1]&&GCD@@#==1&]],{n,0,15}]