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!)
A328673 Number of integer partitions of n in which no two distinct parts are relatively prime. 5
1, 1, 2, 2, 3, 2, 5, 2, 6, 4, 9, 2, 15, 2, 17, 10, 23, 2, 39, 2, 46, 18, 58, 2, 95, 8, 103, 31, 139, 2, 219, 3, 232, 59, 299, 22, 452, 4, 492, 104, 645, 5, 920, 5, 1006, 204, 1258, 8, 1785, 21, 1994, 302, 2442, 11, 3366, 71, 3738, 497, 4570, 18, 6253, 24, 6849 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A partition with no two distinct parts relatively prime is said to be intersecting.

LINKS

Table of n, a(n) for n=0..62.

FORMULA

a(n > 0) = A200976(n) + 1.

EXAMPLE

The a(1) = 1 through a(10) = 9 partitions (A = 10):

  1  2   3    4     5      6       7        8         9          A

     11  111  22    11111  33      1111111  44        63         55

              1111         42               62        333        64

                           222              422       111111111  82

                           111111           2222                 442

                                            11111111             622

                                                                 4222

                                                                 22222

                                                                 1111111111

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], And@@(GCD[##]>1&)@@@Subsets[Union[#], {2}]&]], {n, 0, 20}]

CROSSREFS

The Heinz numbers of these partitions are A328867 (strict case is A318719).

The relatively prime case is A328672.

The strict case is A318717.

The version for non-isomorphic multiset partitions is A319752.

The version for set-systems is A305843.

The version involving all parts (not just distinct ones) is A200976.

Cf. A000837, A202425, A305148, A305854, A306006, A316476, A326910.

Sequence in context: A062830 A322366 A164941 * A115119 A066656 A164896

Adjacent sequences:  A328670 A328671 A328672 * A328674 A328675 A328676

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 29 2019

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 February 23 16:23 EST 2020. Contains 332177 sequences. (Running on oeis4.)