cp's OEIS Frontend

A355973 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.

%I A355973 #22 Apr 13 2024 16:16:57
%S A355973 351,623,5075,5535,21231,69237,78205,88479,89975,101239,173555,286011,
%T A355973 339183,357471,625583,687245,1349487,1415583,2527343,3094039,5426415,
%U A355973 5648031,5721183,5764651,6157723,8512457,10137575,10974951,11365839,11775915,14760911,18617337,21587823,21734127,22649247
%N A355973 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 A355973 This is the base-2 equivalent of A009944.
%H A355973 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 A355973 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 A355973 See the attached text file for other examples.
%t A355973 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 A355973 (Python)
%o A355973 from sympy import divisors
%o A355973 def ok(n):
%o A355973     if not n&1: return False
%o A355973     t = bin(n)[2:][::-1]
%o A355973     return any(t==bin(d)[2:]+bin(n//d)[2:] for d in divisors(n, generator=True))
%o A355973 print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, Apr 13 2024
%Y A355973 Cf. A009944, A030190, A210959, A027750.
%K A355973 nonn,base
%O A355973 1,1
%A A355973 _Scott R. Shannon_, Jul 21 2022