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%I #6 Nov 01 2019 18:41:23
%S 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,
%T 159,169,218,225,289,304,369,400,486,520,636,680,806,873,1051,1105,
%U 1333,1424,1664,1803,2122,2253,2659,2841,3283,3560,4118,4388,5096
%N Number of relatively prime integer partitions of n whose distinct parts are pairwise indivisible.
%e The a(4) = 1 through a(11) = 11 partitions:
%e 1111 32 111111 43 53 54 73 65
%e 11111 52 332 72 433 74
%e 322 11111111 522 532 83
%e 1111111 3222 3322 92
%e 111111111 1111111111 443
%e 533
%e 722
%e 3332
%e 5222
%e 32222
%e 11111111111
%t stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t Table[Length[Select[IntegerPartitions[n],GCD@@#==1&&stableQ[#,Divisible]&]],{n,30}]
%Y The Heinz numbers of these partitions are given by A328677.
%Y The strict case is A328678.
%Y The binary index version is A328671.
%Y Relatively prime partitions are A000837.
%Y Partitions whose distinct parts are pairwise indivisible are A305148.
%Y Cf. A285573, A289509, A303362, A316476, A326912, A327393, A328171.
%K nonn
%O 1,5
%A _Gus Wiseman_, Oct 29 2019
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