cp's OEIS Frontend

A328871 Number of integer partitions of n whose distinct parts are pairwise indivisible (stable) and pairwise non-relatively prime (intersecting).

%I A328871 #6 Nov 12 2019 19:23:29
%S A328871 1,1,2,2,3,2,4,2,4,3,5,2,6,2,7,5,7,2,10,2,11,7,14,2,16,4,19,8,22,2,30,
%T A328871 3,29,14,37,8,48,4,50,19,59,5,82,4,81,28,93,8,128,9,128,38,147,8,199,
%U A328871 19,196,52,223,12,308
%N A328871 Number of integer partitions of n whose distinct parts are pairwise indivisible (stable) and pairwise non-relatively prime (intersecting).
%C A328871 A partition with no two distinct parts divisible is said to be stable, and a partition with no two distinct parts relatively prime is said to be intersecting, so these are just stable intersecting partitions.
%e A328871 The a(1) = 1 through a(10) = 5 partitions (A = 10):
%e A328871   1  2   3    4     5      6       7        8         9          A
%e A328871      11  111  22    11111  33      1111111  44        333        55
%e A328871               1111         222              2222      111111111  64
%e A328871                            111111           11111111             22222
%e A328871                                                                  1111111111
%t A328871 stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t A328871 Table[Length[Select[IntegerPartitions[n],stableQ[Union[#],Divisible]&&stableQ[Union[#],GCD[#1,#2]==1&]&]],{n,0,30}]
%Y A328871 The Heinz numbers of these partitions are A329366.
%Y A328871 Replacing "intersecting" with "relatively prime" gives A328676.
%Y A328871 Stable partitions are A305148.
%Y A328871 Intersecting partitions are A328673.
%Y A328871 Cf. A000837, A285573, A303362, A305148, A316476, A328671, A328677.
%K A328871 nonn
%O A328871 0,3
%A A328871 _Gus Wiseman_, Nov 12 2019