login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A338333 Number of relatively prime 3-part strict integer partitions of n with no 1's. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,12

COMMENTS

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

LINKS

Table of n, a(n) for n=0..63.

EXAMPLE

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

MATHEMATICA

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

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.

Sequence in context: A267261 A219027 A341949 * A287144 A085893 A341950

Adjacent sequences:  A338330 A338331 A338332 * A338334 A338335 A338336

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 30 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 9 06:30 EDT 2021. Contains 343692 sequences. (Running on oeis4.)