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A325106
Number of divisible binary-containment pairs of positive integers up to n.
20
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
0,6
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.
FORMULA
a(n) = A325101(n) - n.
EXAMPLE
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}
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 28 2019
STATUS
approved