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A085721 Semiprimes whose prime factors have an equal number of digits in binary representation.

%I A085721 #32 Jul 07 2023 18:57:12
%S A085721 4,6,9,25,35,49,121,143,169,289,323,361,391,437,493,527,529,551,589,
%T A085721 667,713,841,899,961,1369,1517,1591,1681,1739,1763,1849,1927,1961,
%U A085721 2021,2173,2183,2209,2257,2279,2419,2491,2501,2537,2623,2773,2809
%N A085721 Semiprimes whose prime factors have an equal number of digits in binary representation.
%C A085721 A138510(A174956(a(n))) <= 2. - _Reinhard Zumkeller_, Dec 19 2014
%H A085721 Reinhard Zumkeller, <a href="/A085721/b085721.txt">Table of n, a(n) for n = 1..1000</a>
%H A085721 Dario A. Alpern, <a href="https://www.alpertron.com.ar/BRILLIANT.HTM">Brilliant Numbers</a>.
%e A085721 A078972(35) = 527 = 17*31 -> 10001*11111, therefore 527 is a term;
%e A085721 A078972(37) = 533 = 13*41 -> 1101*101001, therefore 533 is not a term;
%e A085721 A001358(1920) = 7169 = 67*107 -> 1000011*1101011: therefore 7169 a term, but not of A078972.
%t A085721 fQ[n_] := Block[{fi = FactorInteger@ n}, Plus @@ Last /@ fi == 2 && IntegerLength[ fi[[1, 1]], 2] == IntegerLength[ fi[[-1, 1]], 2]]; Select[ Range@ 2866, fQ] (* _Robert G. Wilson v_, Oct 29 2011 *)
%t A085721 Select[Range@ 3000, And[Length@ # == 2, IntegerLength[#1, 2] == IntegerLength[#2, 2] & @@ #] &@ Flatten@ Map[ConstantArray[#1, #2] & @@ # &, FactorInteger@ #] &] (* _Michael De Vlieger_, Oct 08 2016 *)
%o A085721 (PARI) is(n)=bigomega(n)==2&&#binary(factor(n)[1,1])==#binary(n/factor(n)[1,1]) \\ _Charles R Greathouse IV_, Nov 08 2011
%o A085721 (Haskell)
%o A085721 a085721 n = a085721_list !! (n-1)
%o A085721 a085721_list = [p*q | (p,q) <- zip a084126_list a084127_list,
%o A085721                       a070939 p == a070939 q]
%o A085721 -- _Reinhard Zumkeller_, Nov 10 2013
%Y A085721 Cf. A078972, A007088, A070939, A055642.
%Y A085721 Cf. A084126, A084127, A070939.
%Y A085721 Cf. A138510, A174956.
%Y A085721 Cf. A261073, A261074, A261075 (subsequences).
%Y A085721 Intersection of A001358 and A266346.
%K A085721 nonn,base,look
%O A085721 1,1
%A A085721 _Reinhard Zumkeller_, Jul 20 2003
%E A085721 Edited by _Charles R Greathouse IV_, Aug 02 2010