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.

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

Offset

1,1

Comments

There are thirty-nine 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 thirty-nine terms is 495; it is unknown if more exist.

Links

Table of n, a(n) for n=1..38.

Scott R. Shannon, Divisor products of the first thirty-nine terms. These are all the numbers up to 100 million.

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

Cf. A356176, A355791, A355790, A355852, A355857, A030190, A355852, A210959, A027750.

Sequence in context: A325932 A109024 A249190 * A254465 A063334 A181262

Adjacent sequences: A356140 A356141 A356142 * A356144 A356145 A356146

Keyword

nonn,base

Author

Scott R. Shannon, Jul 30 2022

Status

approved