A337452 Number of relatively prime strict integer partitions of n with no 1's.

0, 0, 0, 0, 0, 1, 0, 2, 1, 3, 2, 6, 3, 9, 7, 11, 11, 20, 15, 28, 24, 35, 36, 55, 47, 73, 71, 95, 96, 136, 123, 180, 177, 226, 235, 305, 299, 403, 406, 503, 523, 668, 662, 852, 873, 1052, 1115, 1370, 1391, 1720, 1784, 2125, 2252, 2701, 2786, 3348, 3520, 4116

Offset

0,8

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..300

Example

The a(5) = 1 through a(16) = 11 partitions (A = 10, B = 11, C = 12, D = 13):
  32  43  53  54   73   65   75   76   95    87    97
      52      72   532  74   543  85   B3    B4    B5
              432       83   732  94   653   D2    D3
                        92        A3   743   654   754
                        542       B2   752   753   763
                        632       643  932   762   853
                                  652  5432  843   943
                                  742        852   952
                                  832        942   B32
                                             A32   6532
                                             6432  7432

Mathematica

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

Crossrefs

A078374 is the version allowing 1's.

A302698 is the non-strict version.

A332004 is the ordered version allowing 1's.

A337450 is the ordered non-strict version.

A337451 is the ordered version.

A337485 is the pairwise coprime version.

A000837 counts relatively prime partitions.

A078374 counts relatively prime strict partitions.

A002865 counts partitions with no 1's.

A212804 counts compositions with no 1's.

A291166 appears to rank relatively prime compositions.

A337561 counts pairwise coprime strict compositions.

Cf. A007359, A101268, A289509, A337485, A337563.

Sequence in context: A098911 A052305 A165045 * A164768 A006208 A026805

Adjacent sequences: A337449 A337450 A337451 * A337453 A337454 A337455

Keyword

nonn

Author

Gus Wiseman, Aug 31 2020

Status

approved