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%I #7 Oct 26 2019 10:00:30
%S 6,12,18,20,22,24,28,30,40,48,56,66,68,70,72,76,78,80,82,84,86,88,92,
%T 94,96,104,108,110,112,114,116,118,120,124,126,132,144,148,156,160,
%U 172,176,180,188,192,196,204,208,212,220,224,236,240,244,252,258,264
%N Numbers whose binary indices have no part circularly followed by a divisor or a multiple.
%C A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.
%C Circularity means the last part is followed by the first.
%C Note that this is a somewhat degenerate case, as a part could only be followed by a divisor if it is the last part followed by the first.
%e The sequence of terms together with their binary expansions and binary indices begins:
%e 6: 110 ~ {2,3}
%e 12: 1100 ~ {3,4}
%e 18: 10010 ~ {2,5}
%e 20: 10100 ~ {3,5}
%e 22: 10110 ~ {2,3,5}
%e 24: 11000 ~ {4,5}
%e 28: 11100 ~ {3,4,5}
%e 30: 11110 ~ {2,3,4,5}
%e 40: 101000 ~ {4,6}
%e 48: 110000 ~ {5,6}
%e 56: 111000 ~ {4,5,6}
%e 66: 1000010 ~ {2,7}
%e 68: 1000100 ~ {3,7}
%e 70: 1000110 ~ {2,3,7}
%e 72: 1001000 ~ {4,7}
%e 76: 1001100 ~ {3,4,7}
%e 78: 1001110 ~ {2,3,4,7}
%e 80: 1010000 ~ {5,7}
%e 82: 1010010 ~ {2,5,7}
%e 84: 1010100 ~ {3,5,7}
%t Select[Range[100],!MatchQ[Append[Join@@Position[Reverse[IntegerDigits[#,2]],1],1+IntegerExponent[#,2]],{___,x_,y_,___}/;Divisible[x,y]||Divisible[y,x]]&]
%Y The composition version is A328599.
%Y The necklace composition version is A328601.
%Y Compositions with no consecutive divisors or multiples are A328508.
%Y Numbers whose binary indices are pairwise indivisible are A326704.
%Y Cf. A000031, A318726, A318729, A328171, A328460, A328593, A328598, A328600, A328603.
%K nonn
%O 1,1
%A _Gus Wiseman_, Oct 25 2019
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