A337451 Number of relatively prime strict compositions of n with no 1's.

0, 0, 0, 0, 0, 2, 0, 4, 2, 10, 8, 20, 14, 34, 52, 72, 90, 146, 172, 244, 390, 502, 680, 956, 1218, 1686, 2104, 3436, 4078, 5786, 7200, 10108, 12626, 17346, 20876, 32836, 38686, 53674, 67144, 91528, 113426, 152810, 189124, 245884, 343350, 428494, 552548, 719156

Offset: 0

Author

Gus Wiseman, Aug 31 2020

Keywords

• nonn

Comments

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

Examples

			The a(5) = 2 through a(10) = 8 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)         (5,4)    (2,3,5)
            (5,2)         (7,2)    (2,5,3)
                          (2,3,4)  (3,2,5)
                          (2,4,3)  (3,5,2)
                          (3,2,4)  (5,2,3)
                          (3,4,2)  (5,3,2)
                          (4,2,3)
                          (4,3,2)
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..350

Crossrefs

A032022 does not require relative primality.

A302698 is the unordered non-strict version.

A332004 is the version allowing 1's.

A337450 is the non-strict version.

A337452 is the unordered version.

A000837 counts relatively prime partitions.

A032020 counts strict compositions.

A078374 counts strict relatively prime partitions.

A002865 counts partitions with no 1's.

A212804 counts compositions with no 1's.

A291166 appears to rank relatively prime compositions.

A337462 counts pairwise coprime compositions.

A337561 counts strict pairwise coprime compositions.

Cf. A000010, A007359, A101268, A178472, A216652, A289509, A337562, A337563.

Programs

Mathematica

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