A355852 - OEIS

A355852

Numbers that can be written as the product of two of its divisors such that the binary value of the number has the same length as the concatenation of the binary values of the divisors and differs by only one bit from the divisor concatenation.

%I #36 Jul 26 2022 12:51:06

%S 39,78,87,156,174,183,312,348,366,375,399,539,624,696,732,750,759,798,

%T 847,1053,1078,1248,1392,1464,1500,1518,1527,1596,1694,1743,2106,2156,

%U 2496,2784,2928,3000,3036,3054,3063,3192,3388,3486,3535,3615,4212,4312,4381,4992,5175,5568,5856,6000

%N Numbers that can be written as the product of two of its divisors such that the binary value of the number has the same length as the concatenation of the binary values of the divisors and differs by only one bit from the divisor concatenation.

%C See A355857 for the smallest number that shares n out of n+1 bits with the divisor binary concatenation.

%H Michael De Vlieger, <a href="/A355852/a355852.png">Plot of a(n) expanded in binary</a>, black pixels indicating 1's and white 0's, with n on the x-axis and 2^y increasing from bottom to top.

%H Scott R. Shannon, <a href="/A355852/a355852_1.txt">Divisor products for the first 1217 terms</a>. These are all the terms up to 100000000.

%e 39 is a term as 39 = 100111_2 = 13 * 3 = 1101_2 * 11_2, and "100111" has five bits out of six in common with "110111".

%e 539 is a term as 539 = 1000011011_2 = 49 * 11 = 110001_2 * 1011_2 and "1000011011" has nine out of ten bits in common with "1100011011".

%e See the attached text file for other examples.

%t Select[Range[6000], Function[{m, d}, 0 < Count[Map[Join @@ IntegerDigits[{##}, 2] & @@ {#, m/#} &, Divisors[m]], _?(Length[#] == Length[d] && Total[BitXor @@ {#, d}] == 1 &)]] @@ {#, IntegerDigits[#, 2]} &] (* _Michael De Vlieger_, Jul 21 2022 *)

%Y Cf. A355857, A030190, A210959, A027750.

%K nonn

%O 1,1

%A _Scott R. Shannon_ and _Michael De Vlieger_, Jul 19 2022