

A356143


Numbers that can be written in two or more ways as the product of three divisors greater than 1 such that the number in binary is contained in the string concatenation of the divisors in binary.


2



126, 252, 495, 504, 1008, 2016, 3420, 3510, 4032, 5850, 8064, 11700, 16128, 23400, 32256, 46800, 64512, 93600, 129024, 187200, 258048, 374400, 516096, 748800, 1032192, 1497600, 2064384, 2995200, 4128768, 5990400, 8257536, 11980800, 16515072, 23961600, 33030144, 47923200, 57587274, 66060288
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OFFSET

1,1


COMMENTS

There are thirtynine terms less than 100 million  the terms in the data section along with 95846400. All of these numbers have two ways that they can be written to satisfy their binary value being contained in the binary concatenation of the three divisors; it is unknown if numbers exist that can be written in three or more ways that satisfy this criterion. The only odd number in the first thirtynine terms is 495; it is unknown if more exist.


LINKS



EXAMPLE

126 is a term as 126 = 1111110_2 = 3 * 3 * 14 = 11_2 * 11_2 * 1110_2 = 3 * 7 * 6 = 11_2 * 111_2 * 110_2 and "11" + "11" + "1110" = "11111110" contains "1111110" and "11" + "111" + "110" = "11111110" contains "1111110".
3420 is a term as 3420 = 110101011100_2 = 5 * 171 * 4 = 101_2 * 10101011_2 * 100_2 = 6 * 10 * 57 = 110_2 * 1010_2 * 111001_2 and "101" + "10101011" + "100" = "10110101011100" contains "110101011100" and "110" + "1010" + "111001" = "1101010111001" contains "110101011100".
See the attached text file for other examples.


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



