A325106 Number of divisible binary-containment pairs of positive integers up to n.

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, 26, 27, 28, 31, 32, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 48, 49, 50, 51, 52, 53, 56, 57, 58, 61, 63, 64, 65, 66, 67, 70, 71, 72, 77, 77, 78, 79, 80, 81

Offset: 0

Author

Gus Wiseman, Mar 28 2019

Keywords

• nonn

Comments

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.

Examples

			The a(3) = 1 through a(12) = 8 pairs:
  {1,3}  {1,3}  {1,3}  {1,3}  {1,3}  {1,3}  {1,3}  {1,3}   {1,3}   {1,3}
                {1,5}  {1,5}  {1,5}  {1,5}  {1,5}  {1,5}   {1,5}   {1,5}
                       {2,6}  {1,7}  {1,7}  {1,7}  {1,7}   {1,7}   {1,7}
                              {2,6}  {2,6}  {1,9}  {1,9}   {1,9}   {1,9}
                                            {2,6}  {2,6}   {2,6}   {2,6}
                                                   {2,10}  {1,11}  {1,11}
                                                           {2,10}  {2,10}
                                                                   {4,12}
		

Crossrefs

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

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

Programs

Mathematica

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}]

Formula

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