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.

39, 78, 87, 156, 174, 183, 312, 348, 366, 375, 399, 539, 624, 696, 732, 750, 759, 798, 847, 1053, 1078, 1248, 1392, 1464, 1500, 1518, 1527, 1596, 1694, 1743, 2106, 2156, 2496, 2784, 2928, 3000, 3036, 3054, 3063, 3192, 3388, 3486, 3535, 3615, 4212, 4312, 4381, 4992, 5175, 5568, 5856, 6000

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..52.

Michael De Vlieger, Plot of a(n) expanded in binary, black pixels indicating 1's and white 0's, with n on the x-axis and 2^y increasing from bottom to top.

Scott R. Shannon, Divisor products for the first 1217 terms. These are all the terms up to 100000000.

Example

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".
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".
See the attached text file for other examples.

Mathematica

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 *)

Crossrefs

Cf. A355857, A030190, A210959, A027750.

Sequence in context: A044105 A044486 A072122 * A290815 A355857 A354227

Adjacent sequences: A355849 A355850 A355851 * A355853 A355854 A355855

Keyword

nonn

Author

Scott R. Shannon and Michael De Vlieger, Jul 19 2022

Status

approved