A307230 - OEIS

%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