A328676 Number of relatively prime integer partitions of n whose distinct parts are pairwise indivisible.

1, 1, 1, 1, 2, 1, 4, 3, 5, 5, 11, 7, 16, 14, 18, 22, 34, 30, 47, 45, 59, 66, 89, 90, 118, 125, 159, 169, 218, 225, 289, 304, 369, 400, 486, 520, 636, 680, 806, 873, 1051, 1105, 1333, 1424, 1664, 1803, 2122, 2253, 2659, 2841, 3283, 3560, 4118, 4388, 5096

Offset: 1

Author

Gus Wiseman, Oct 29 2019

Keywords

• nonn

Examples

			The a(4) = 1 through a(11) = 11 partitions:
  1111  32     111111  43       53        54         73          65
        11111          52       332       72         433         74
                       322      11111111  522        532         83
                       1111111            3222       3322        92
                                          111111111  1111111111  443
                                                                 533
                                                                 722
                                                                 3332
                                                                 5222
                                                                 32222
                                                                 11111111111
		

Crossrefs

The Heinz numbers of these partitions are given by A328677.

The strict case is A328678.

The binary index version is A328671.

Relatively prime partitions are A000837.

Partitions whose distinct parts are pairwise indivisible are A305148.

Cf. A285573, A289509, A303362, A316476, A326912, A327393, A328171.

Programs

Mathematica

stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
Table[Length[Select[IntegerPartitions[n],GCD@@#==1&&stableQ[#,Divisible]&]],{n,30}]