This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A325123 #12 Jul 27 2019 14:57:51
%S A325123 0,0,1,1,3,3,4,4,7,7,9,9,12,12,13,13,17,17,19,19,22,22,23,23,28,28,29,
%T A325123 29,31,31,32,32,37,37,39,39,44,44,45,45,50,50,52,52,54,54,55,55,62,62,
%U A325123 64,64,66,66,68,68,72,72,73,73,76,76,77,77,83,83,85,85
%N A325123 Number of divisible pairs of positive integers up to n with no binary carries.
%C A325123 Two positive integers are divisible if the first divides the second, and they have a binary carry if the positions of 1's in their reversed binary expansion overlap.
%C A325123 a(2k+1) = a(2k), since an odd number and any divisor will overlap in the last digit. Additionally, a(2k+2) > a(2k+1) because the pair {1,2k+2} is always valid. Therefore, every term appears exactly twice. - _Charlie Neder_, Apr 02 2019
%e A325123 The a(2) = 1 through a(11) = 9 pairs:
%e A325123 {1,2} {1,2} {1,2} {1,2} {1,2} {1,2} {1,2} {1,2} {1,2} {1,2}
%e A325123 {1,4} {1,4} {1,4} {1,4} {1,4} {1,4} {1,4} {1,4}
%e A325123 {2,4} {2,4} {1,6} {1,6} {1,6} {1,6} {1,6} {1,6}
%e A325123 {2,4} {2,4} {1,8} {1,8} {1,8} {1,8}
%e A325123 {2,4} {2,4} {2,4} {2,4}
%e A325123 {2,8} {2,8} {2,8} {2,8}
%e A325123 {4,8} {4,8} {4,8} {4,8}
%e A325123 {1,10} {1,10}
%e A325123 {5,10} {5,10}
%t A325123 Table[Length[Select[Tuples[Range[n],2],Divisible@@Reverse[#]&&Intersection[Position[Reverse[IntegerDigits[#[[1]],2]],1],Position[Reverse[IntegerDigits[#[[2]],2]],1]]=={}&]],{n,0,20}]
%Y A325123 Cf. A006218, A019565, A050315, A070939, A080572, A247935, A267610.
%Y A325123 Cf. A325095, A325096, A325101, A325103, A325104, A325105, A325106, A325124.
%K A325123 nonn
%O A325123 0,5
%A A325123 _Gus Wiseman_, Mar 29 2019