cp's OEIS Frontend

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.

%I A356143 #26 Jul 30 2022 14:14:47
%S A356143 126,252,495,504,1008,2016,3420,3510,4032,5850,8064,11700,16128,23400,
%T A356143 32256,46800,64512,93600,129024,187200,258048,374400,516096,748800,
%U A356143 1032192,1497600,2064384,2995200,4128768,5990400,8257536,11980800,16515072,23961600,33030144,47923200,57587274,66060288
%N 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.
%C A356143 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.
%H A356143 Scott R. Shannon, <a href="/A356143/a356143.txt">Divisor products of the first thirty-nine terms</a>. These are all the numbers up to 100 million.
%e A356143 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".
%e A356143 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".
%e A356143 See the attached text file for other examples.
%Y A356143 Cf. A356176, A355791, A355790, A355852, A355857, A030190, A355852, A210959, A027750.
%K A356143 nonn,base
%O A356143 1,1
%A A356143 _Scott R. Shannon_, Jul 30 2022