A325101 Number of divisible binary-containment pairs of positive integers up to n.

0, 1, 2, 4, 5, 7, 9, 11, 12, 14, 16, 18, 20, 22, 24, 28, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 53, 55, 57, 61, 63, 64, 66, 68, 70, 72, 74, 76, 79, 81, 83, 85, 87, 89, 93, 95, 97, 99, 101, 103, 107, 109, 111, 115, 118, 120, 122, 124, 126, 130, 132, 134

Offset

0,3

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 those in the second.

Links

Table of n, a(n) for n=0..62.

Formula

a(n) = A325106(n) + n.

Example

The a(1) = 1 through a(8) = 12 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)  (4,4)  (3,3)  (3,3)
                                     (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[#[[2]], #[[1]]]&&SubsetQ[Position[Reverse[IntegerDigits[#[[2]], 2]], 1], Position[Reverse[IntegerDigits[#1[[1]], 2]], 1]]&]], {n, 0, 30}]

Crossrefs

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

Cf. A325094, A325102, A325106, A325107, A325108, A325109, A325110.

Sequence in context: A047379 A093848 A049039 * A301728 A005152 A060831

Adjacent sequences: A325098 A325099 A325100 * A325102 A325103 A325104

Keyword

nonn

Author

Gus Wiseman, Mar 28 2019

Status

approved