login
A307230
Number of divisible pairs of distinct positive integers up to n with at least one binary carry.
1
0, 0, 0, 1, 1, 2, 4, 5, 5, 7, 8, 9, 11, 12, 14, 17, 17, 18, 21, 22, 24, 27, 29, 30, 32, 34, 36, 39, 42, 43, 49, 50, 50, 53, 54, 57, 60, 61, 63, 66, 68, 69, 74, 75, 78, 83, 85, 86, 88, 90, 93, 96, 99, 100, 105, 108, 111, 114, 116, 117, 125, 126, 128, 133, 133
OFFSET
0,6
COMMENTS
Two positive integers are divisible if the first divides the second, and have a binary carry if the positions of 1's in their reversed binary expansion overlap.
FORMULA
a(n) = A325124(n) - n.
EXAMPLE
The a(3) = 1 through a(12) = 11 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}
{3,6} {2,6} {2,6} {1,9} {1,9} {1,9} {1,9}
{3,6} {3,6} {2,6} {2,6} {2,6} {2,6}
{3,6} {3,6} {3,6} {3,6}
{3,9} {3,9} {3,9} {3,9}
{2,10} {1,11} {1,11}
{2,10} {2,10}
{4,12}
{6,12}
MATHEMATICA
Table[Length[Select[Subsets[Range[n], {2}], Divisible@@Reverse[#]&&Intersection[Position[Reverse[IntegerDigits[#[[1]], 2]], 1], Position[Reverse[IntegerDigits[#[[2]], 2]], 1]]!={}&]], {n, 0, 20}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 29 2019
STATUS
approved