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Number of divisible binary-containment pairs of positive integers up to n.
20

%I #8 Jul 27 2019 14:57:51

%S 0,0,0,1,1,2,3,4,4,5,6,7,8,9,10,13,13,14,15,16,17,18,19,20,21,22,23,

%T 26,27,28,31,32,32,33,34,35,36,37,38,40,41,42,43,44,45,48,49,50,51,52,

%U 53,56,57,58,61,63,64,65,66,67,70,71,72,77,77,78,79,80,81

%N Number of divisible binary-containment pairs of positive integers up to n.

%C A pair of positive integers is divisible if the first divides the second, and is a binary containment if the positions of 1's in the reversed binary expansion of the first are a subset of the positions of 1's in the reversed binary expansion of the second.

%F a(n) = A325101(n) - n.

%e The a(3) = 1 through a(12) = 8 pairs:

%e {1,3} {1,3} {1,3} {1,3} {1,3} {1,3} {1,3} {1,3} {1,3} {1,3}

%e {1,5} {1,5} {1,5} {1,5} {1,5} {1,5} {1,5} {1,5}

%e {2,6} {1,7} {1,7} {1,7} {1,7} {1,7} {1,7}

%e {2,6} {2,6} {1,9} {1,9} {1,9} {1,9}

%e {2,6} {2,6} {2,6} {2,6}

%e {2,10} {1,11} {1,11}

%e {2,10} {2,10}

%e {4,12}

%t Table[Length[Select[Subsets[Range[n],{2}],Divisible[#[[2]],#[[1]]]&&SubsetQ[Position[Reverse[IntegerDigits[#[[2]],2]],1],Position[Reverse[IntegerDigits[#1[[1]],2]],1]]&]],{n,0,30}]

%Y Cf. A000005, A006218, A080572, A267610, A267700.

%Y Cf. A325094, A325101, A325102, A325107, A325108, A325109, A325110.

%K nonn

%O 0,6

%A _Gus Wiseman_, Mar 28 2019