A265236 Number of solutions to the equation A x B = C, where A, B and C are nonnegative numbers appearing as (contiguous) substrings of the binary representation of n.

1, 1, 8, 3, 13, 12, 18, 5, 19, 17, 18, 20, 31, 26, 28, 7, 26, 23, 23, 26, 31, 22, 32, 28, 47, 40, 38, 34, 49, 40, 38, 9, 34, 30, 29, 31, 31, 31, 38, 34, 47, 39, 28, 34, 53, 40, 46, 38, 66, 55, 54, 48, 59, 46, 46, 48, 75, 62, 58, 52, 67, 58, 48, 11, 43, 38

Offset: 0

Author

Reinhard Zumkeller, Dec 06 2015

Keywords

• nonn

Comments

A, B and C are allowed to be zero, in contrast to A265008;

a(A000225(n)) = A265008(A000225(n));

a(A062289(n)) != A265008(A062289(n)).

Examples

			.  n | A007088 | A119709     |  a |
. ---+---------+-------------+----+-------------------------------------
.  2 |      10 | [0,1,2]     |  8 = #{(0,0,0), (0,1,0), (0,2,0), (1,0,0),
.    |         |             |        (2,0,0), (1,1,1), (1,2,2), (2,1,2)}
.  3 |      11 | [1,3]       |  3 = #{(1,1,1), (1,3,3), (3,1,3)}
.  4 |     100 | [0,1,2,4]   | 13 = #{(0,0,0), (0,1,0), (0,2,0), (0,4,0),
.    |         |             |         (1,0,0), (2,0,0), (4,0,0), (1,1,1),
.    |         |             |         (1,2,2), (2,1,2), (1,4,4), (2,2,4),
.    |         |             |         (4,1,4)}
.  5 |     101 | [0,1,2,5]   | 12 = #{(0,0,0), (0,1,0), (0,2,0), (0,5,0),
.    |         |             |         (1,0,0), (2,0,0), (5,0,0), (1,1,1),
.    |         |             |         (1,2,2), (2,1,2), (1,5,5), (5,1,5)}
.  6 |     110 | [0,1,2,3,6] | 18 = #{(0,0,0), (0,1,0), (0,2,0), (0,3,0),
.    |         |             |         (0,6,0), (1,0,0), (2,0,0), (3,0,0),
.    |         |             |         (6,0,0), (1,1,1), (1,2,2), (2,1,2),
.    |         |             |         (1,3,3), (3,1,3), (1,6,6), (2,3,6),
.    |         |             |         (3,2,6), (6,1,6)}
.  7 |     111 | [1,3,7]     |≈ 5 = #{(1,1,1), (1,3,3), (3,1,3), (1,7,7),
.    |         |             |         (7,1,7)} .
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A007088, A119709, A265008, A265183 (decimal case), A000225, A062289, A043545, A078822.

Programs

Haskell

a265236 n = length [() | let cs = a119709_row n, a <- cs, b <- cs, c <- cs,
                         a * b == c || c == 0 && a * b == 0]

Formula

For n > 0: a(n) = A265008(n) + A043545(n) * (2*A078822(n) - 1).

Extensions

Suggested by N. J. A. Sloane.