

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.


6



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
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OFFSET

1,1


COMMENTS

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


LINKS

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


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



KEYWORD

nonn


AUTHOR



STATUS

approved



