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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 13 03:33 EDT 2024. Contains 375857 sequences. (Running on oeis4.)