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

0,3

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.

Links

Table of n, a(n) for n=0..60.

Formula

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

Example

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)

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}]

Crossrefs

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

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

Sequence in context: A188468 A364132 A285251 * A231013 A231008 A092311

Adjacent sequences: A325121 A325122 A325123 * A325125 A325126 A325127

Keyword

nonn

Author

Gus Wiseman, Mar 29 2019

Status

approved