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A355973
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Numbers that can be written as the product of two of its divisors such that the reverse of the binary value of the number equals the concatenation of the binary values of the divisors.
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2
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351, 623, 5075, 5535, 21231, 69237, 78205, 88479, 89975, 101239, 173555, 286011, 339183, 357471, 625583, 687245, 1349487, 1415583, 2527343, 3094039, 5426415, 5648031, 5721183, 5764651, 6157723, 8512457, 10137575, 10974951, 11365839, 11775915, 14760911, 18617337, 21587823, 21734127, 22649247
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OFFSET
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1,1
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COMMENTS
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This is the base-2 equivalent of A009944.
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LINKS
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EXAMPLE
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351 is a term as 351 = 101011111_2 = 3 * 117 = 11_2 * 1110101_2, and "101011111" in reverse is "111110101" which equals "11" + "1110101".
See the attached text file for other examples.
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MATHEMATICA
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Select[Range[2^18], Function[{k, d, m}, AnyTrue[Map[Join @@ IntegerDigits[#, 2] &, Transpose@ {d, k/d}], # == m &]] @@ {#, Divisors[#], Reverse@ IntegerDigits[#, 2]} &] (* Michael De Vlieger, Jul 23 2022 *)
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PROG
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(Python)
from sympy import divisors
def ok(n):
if not n&1: return False
t = bin(n)[2:][::-1]
return any(t==bin(d)[2:]+bin(n//d)[2:] for d in divisors(n, generator=True))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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