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%I #6 Nov 01 2019 18:41:37
%S 1,0,0,0,1,0,2,1,2,2,4,3,5,4,5,7,10,9,12,11,14,15,22,20,25,26,32,33,
%T 44,41,54,49,62,67,80,80,100,100,118,121,152,148,179,178,210,219,267,
%U 259,316,313,363,380,449,448,529,532,619,640,745,749,867,889
%N Number of strict, pairwise indivisible, relatively prime integer partitions of n.
%C Note that pairwise indivisibility implies strictness, but we include "strict" in the name in order to more clearly distinguish it from A328676 = "Number of relatively prime integer partitions of n whose distinct parts are pairwise indivisible".
%F Moebius transform of A303362.
%e The a(1) = 1 through a(20) = 11 partitions (A..H = 10..20) (empty columns not shown):
%e 1 32 43 53 54 73 65 75 76 95 87 97 98 B7 A9 B9
%e 52 72 532 74 543 85 B3 B4 B5 A7 D5 B8 D7
%e 83 732 94 743 D2 D3 B6 765 C7 H3
%e 92 A3 752 654 754 C5 873 D6 875
%e B2 753 853 D4 954 E5 965
%e 952 E3 972 F4 974
%e B32 F2 B43 G3 A73
%e 764 B52 H2 B54
%e A43 D32 865 B72
%e 7532 964 D43
%e B53 D52
%e 7543
%t stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&GCD@@#==1&&stableQ[#,Divisible]&]],{n,30}]
%Y The Heinz numbers of these partitions are the squarefree terms of A328677.
%Y The non-strict case is A328676.
%Y Pairwise indivisible partitions are A303362.
%Y Strict, relatively prime partitions are A078374.
%Y A ranking function using binary indices is A328671.
%Y Cf. A000837, A285572, A285573, A304713, A305148, A316476, A328171.
%K nonn
%O 1,7
%A _Gus Wiseman_, Oct 30 2019
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