A325124 Number of divisible pairs of positive integers up to n with at least one binary carry.

0, 1, 2, 4, 5, 7, 10, 12, 13, 16, 18, 20, 23, 25, 28, 32, 33, 35, 39, 41, 44, 48, 51, 53, 56, 59, 62, 66, 70, 72, 79, 81, 82, 86, 88, 92, 96, 98, 101, 105, 108, 110, 116, 118, 122, 128, 131, 133, 136, 139, 143, 147, 151, 153, 159, 163, 167, 171, 174, 176, 185

Offset: 0

Author

Gus Wiseman, Mar 29 2019

Keywords

• nonn

Comments

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.

Examples

			The a(1) = 1 through a(8) = 13 pairs:
  (1,1)  (1,1)  (1,1)  (1,1)  (1,1)  (1,1)  (1,1)  (1,1)
         (2,2)  (1,3)  (1,3)  (1,3)  (1,3)  (1,3)  (1,3)
                (2,2)  (2,2)  (1,5)  (1,5)  (1,5)  (1,5)
                (3,3)  (3,3)  (2,2)  (2,2)  (1,7)  (1,7)
                       (4,4)  (3,3)  (2,6)  (2,2)  (2,2)
                              (4,4)  (3,3)  (2,6)  (2,6)
                              (5,5)  (3,6)  (3,3)  (3,3)
                                     (4,4)  (3,6)  (3,6)
                                     (5,5)  (4,4)  (4,4)
                                     (6,6)  (5,5)  (5,5)
                                            (6,6)  (6,6)
                                            (7,7)  (7,7)
                                                   (8,8)
		

Crossrefs

Cf. A006218, A019565, A050315, A070939, A080572, A247935, A267610, A307230.

Cf. A325095, A325096, A325101, A325103, A325104, A325105, A325106, A325123.

Programs

Mathematica

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}]

Formula

a(n) = A307230(n) + n.