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A338315 Number of integer partitions of n with no 1's whose distinct parts are pairwise coprime, where a singleton is not considered coprime unless it is (1). 4
0, 0, 0, 0, 0, 1, 0, 3, 2, 4, 4, 10, 6, 15, 13, 16, 21, 31, 29, 43, 41, 50, 63, 79, 81, 99, 113, 129, 145, 179, 197, 228, 249, 284, 328, 363, 418, 472, 522, 581, 655, 741, 828, 921, 1008, 1123, 1259, 1407, 1546, 1709, 1889, 2077, 2292, 2554, 2799, 3061, 3369 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

The Heinz numbers of these partitions are given by A337987. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), giving a bijective correspondence between positive integers and integer partitions.

LINKS

Table of n, a(n) for n=0..56.

EXAMPLE

The a(5) = 1 through a(13) = 15 partitions (empty column indicated by dot, A = 10, B = 11):

  32   .  43    53    54     73     65      75      76

          52    332   72     433    74      543     85

          322         522    532    83      552     94

                      3222   3322   92      732     A3

                                    443     5322    B2

                                    533     33222   544

                                    722             553

                                    3332            733

                                    5222            922

                                    32222           4333

                                                    5332

                                                    7222

                                                    33322

                                                    52222

                                                    322222

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], !MemberQ[#, 1]&&CoprimeQ@@Union[#]&]], {n, 0, 30}]

CROSSREFS

A200976 is a pairwise non-coprime instead of pairwise coprime version.

A304709 allows 1's, with strict case A305713 and Heinz numbers A304711.

A318717 counts pairwise non-coprime strict partitions.

A337485 is the strict version, with Heinz numbers A337984.

A337987 gives the Heinz numbers of these partitions.

A338317 considers singletons coprime, with Heinz numbers A338316.

A007359 counts singleton or pairwise coprime partitions with no 1's.

A327516 counts pairwise coprime partitions, ranked by A302696.

A328673 counts partitions with no two distinct parts relatively prime.

A337462 counts pairwise coprime compositions, ranked by A333227.

A337561 counts pairwise coprime strict compositions.

A337665 counts compositions whose distinct parts are pairwise coprime.

A337667 counts pairwise non-coprime compositions, ranked by A337666.

A337697 counts pairwise coprime compositions with no 1's.

Cf. A051424, A101268, A220377, A302568, A328867, A333228, A337563.

Sequence in context: A195472 A240538 A326923 * A240541 A073369 A021759

Adjacent sequences:  A338312 A338313 A338314 * A338316 A338317 A338318

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 23 2020

STATUS

approved

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Last modified June 13 20:25 EDT 2021. Contains 345009 sequences. (Running on oeis4.)