A338333 Number of relatively prime 3-part strict integer partitions of n with no 1's.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 4, 7, 6, 10, 8, 14, 12, 18, 16, 24, 18, 30, 25, 34, 30, 44, 31, 52, 42, 56, 49, 69, 50, 80, 64, 83, 70, 102, 71, 114, 90, 112, 100, 140, 98, 153, 117, 153, 132, 184, 128, 195, 154, 196, 169, 234, 156, 252, 196, 241

Offset: 0

Author

Gus Wiseman, Oct 30 2020

Keywords

• nonn

Comments

The Heinz numbers of these partitions are the intersection of A005117 (strict), A005408 (no 1's), A014612 (length 3), and A289509 (relatively prime).

Examples

			The a(9) = 1 through a(19) = 14 triples (A = 10, B = 11, C = 12, D = 13, E = 14):
  432   532   542   543   643   653   654   754   764   765   865
              632   732   652   743   753   763   854   873   874
                          742   752   762   853   863   954   964
                          832   932   843   943   872   972   973
                                      852   952   953   A53   982
                                      942   B32   962   B43   A54
                                      A32         A43   B52   A63
                                                  A52   D32   A72
                                                  B42         B53
                                                  C32         B62
                                                              C43
                                                              C52
                                                              D42
                                                              E32
		

Crossrefs

A001399(n-9) does not require relative primality.

A005117 /\ A005408 /\ A014612 /\ A289509 gives the Heinz numbers.

A055684 is the 2-part version.

A284825 counts the case that is also pairwise non-coprime.

A337452 counts these partitions of any length.

A337563 is the pairwise coprime instead of relatively prime version.

A337605 is the pairwise non-coprime instead of relative prime version.

A338332 is the not necessarily strict version.

A338333*6 is the ordered version.

A000837 counts relatively prime partitions.

A008284 counts partitions by sum and length.

A078374 counts relatively prime strict partitions.

A101271 counts 3-part relatively prime strict partitions.

A220377 counts 3-part pairwise coprime strict partitions.

A337601 counts 3-part partitions whose distinct parts are pairwise coprime.

Cf. A000010, A000217, A000741, A023022, A082024, A302698, A307719, A337450, A337599, A338468.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n,{3}],UnsameQ@@#&&!MemberQ[#,1]&&GCD@@#==1&]],{n,0,30}]