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A087086 Primitive sets of integers, each subset mapped onto a unique binary integer, values here shown in decimal.

%I A087086 #19 Aug 25 2025 02:12:33
%S A087086 0,1,2,4,6,8,12,16,18,20,22,24,28,32,40,48,56,64,66,68,70,72,76,80,82,
%T A087086 84,86,88,92,96,104,112,120,128,132,144,148,160,176,192,196,208,212,
%U A087086 224,240,256,258,264,272,274,280,288,296,304,312,320,322,328,336,338,344
%N A087086 Primitive sets of integers, each subset mapped onto a unique binary integer, values here shown in decimal.
%C A087086 A primitive set of integers has no pair of elements one of which divides the other. Each element i in a subset contributes 2^(i-1) to the binary value for that subset. The integers missing from the sequence correspond to nonprimitive subsets.
%D A087086 Alan Sutcliffe, Divisors and Common Factors in Sets of Integers, awaiting publication
%e A087086 a(10)=22 since the 10th primitive set counting from 0 is {5,3,2}, which maps onto 10110 binary = 22 decimal.
%e A087086 From _Gus Wiseman_, Oct 31 2019: (Start)
%e A087086 The sequence of terms together with their binary expansions and binary indices begins:
%e A087086    0:       0 ~ {}
%e A087086    1:       1 ~ {1}
%e A087086    2:      10 ~ {2}
%e A087086    4:     100 ~ {3}
%e A087086    6:     110 ~ {2,3}
%e A087086    8:    1000 ~ {4}
%e A087086   12:    1100 ~ {3,4}
%e A087086   16:   10000 ~ {5}
%e A087086   18:   10010 ~ {2,5}
%e A087086   20:   10100 ~ {3,5}
%e A087086   22:   10110 ~ {2,3,5}
%e A087086   24:   11000 ~ {4,5}
%e A087086   28:   11100 ~ {3,4,5}
%e A087086 (End)
%t A087086 stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t A087086 Select[Range[0,100],stableQ[Join@@Position[Reverse[IntegerDigits[#,2]],1],Divisible]&] (* _Gus Wiseman_, Oct 31 2019 *)
%Y A087086 A051026 gives the number of primitive subsets of the integers 1 to n.
%Y A087086 The version for prime indices (rather than binary indices) is A316476.
%Y A087086 The relatively prime case is A328671.
%Y A087086 Partitions with no consecutive divisible parts are A328171.
%Y A087086 Compositions without consecutive divisible parts are A328460.
%Y A087086 A ranking of antichains is A326704.
%Y A087086 Cf. A000120, A048793, A070939, A285572, A285573, A303362, A304713, A305148, A328593.
%K A087086 easy,nonn,base,changed
%O A087086 0,3
%A A087086 Alan Sutcliffe (alansut(AT)ntlworld.com), Aug 14 2003