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%I #22 Apr 13 2024 16:16:57
%S 351,623,5075,5535,21231,69237,78205,88479,89975,101239,173555,286011,
%T 339183,357471,625583,687245,1349487,1415583,2527343,3094039,5426415,
%U 5648031,5721183,5764651,6157723,8512457,10137575,10974951,11365839,11775915,14760911,18617337,21587823,21734127,22649247
%N 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.
%C This is the base-2 equivalent of A009944.
%H Scott R. Shannon, <a href="/A355973/a355973.txt">Divisor products for the first 46 terms</a>. These are all the terms up to 100000000.
%e 351 is a term as 351 = 101011111_2 = 3 * 117 = 11_2 * 1110101_2, and "101011111" in reverse is "111110101" which equals "11" + "1110101".
%e See the attached text file for other examples.
%t 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 *)
%o (Python)
%o from sympy import divisors
%o def ok(n):
%o if not n&1: return False
%o t = bin(n)[2:][::-1]
%o return any(t==bin(d)[2:]+bin(n//d)[2:] for d in divisors(n, generator=True))
%o print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, Apr 13 2024
%Y Cf. A009944, A030190, A210959, A027750.
%K nonn,base
%O 1,1
%A _Scott R. Shannon_, Jul 21 2022
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