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%I #8 Jul 27 2019 14:57:51
%S 0,0,0,1,1,2,4,5,5,7,8,9,11,12,14,17,17,18,21,22,24,27,29,30,32,34,36,
%T 39,42,43,49,50,50,53,54,57,60,61,63,66,68,69,74,75,78,83,85,86,88,90,
%U 93,96,99,100,105,108,111,114,116,117,125,126,128,133,133
%N Number of divisible pairs of distinct positive integers up to n with at least one binary carry.
%C Two positive integers are divisible if the first divides the second, and have a binary carry if the positions of 1's in their reversed binary expansion overlap.
%F a(n) = A325124(n) - n.
%e The a(3) = 1 through a(12) = 11 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 {3,6} {2,6} {2,6} {1,9} {1,9} {1,9} {1,9}
%e {3,6} {3,6} {2,6} {2,6} {2,6} {2,6}
%e {3,6} {3,6} {3,6} {3,6}
%e {3,9} {3,9} {3,9} {3,9}
%e {2,10} {1,11} {1,11}
%e {2,10} {2,10}
%e {4,12}
%e {6,12}
%t Table[Length[Select[Subsets[Range[n],{2}],Divisible@@Reverse[#]&&Intersection[Position[Reverse[IntegerDigits[#[[1]],2]],1],Position[Reverse[IntegerDigits[#[[2]],2]],1]]!={}&]],{n,0,20}]
%Y Cf. A006218, A019565, A050315, A070939, A080572, A247935, A267610.
%Y Cf. A325095, A325096, A325101, A325103, A325104, A325105, A325106, A325124.
%K nonn
%O 0,6
%A _Gus Wiseman_, Mar 29 2019
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