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 A085721 Semiprimes whose prime factors have an equal number of digits in binary representation. 8
 4, 6, 9, 25, 35, 49, 121, 143, 169, 289, 323, 361, 391, 437, 493, 527, 529, 551, 589, 667, 713, 841, 899, 961, 1369, 1517, 1591, 1681, 1739, 1763, 1849, 1927, 1961, 2021, 2173, 2183, 2209, 2257, 2279, 2419, 2491, 2501, 2537, 2623, 2773, 2809 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A138510(A174956(a(n))) <= 2. - Reinhard Zumkeller, Dec 19 2014 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 Dario A. Alpern, Brilliant Numbers. EXAMPLE A078972(35) = 527 = 17*31 -> 10001*11111, therefore 527 is a term; A078972(37) = 533 = 13*41 -> 1101*101001, therefore 533 is not a term; A001358(1920) = 7169 = 67*107 -> 1000011*1101011: therefore 7169 a term, but not of A078972. MATHEMATICA 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 *) Select[Range@ 3000, And[Length@ # == 2, IntegerLength[#1, 2] == IntegerLength[#2, 2] & @@ #] &@ Flatten@ Map[ConstantArray[#1, #2] & @@ # &, FactorInteger@ #] &] (* Michael De Vlieger, Oct 08 2016 *) PROG (PARI) is(n)=bigomega(n)==2&&#binary(factor(n)[1, 1])==#binary(n/factor(n)[1, 1]) \\ Charles R Greathouse IV, Nov 08 2011 (Haskell) a085721 n = a085721_list !! (n-1) a085721_list = [p*q | (p, q) <- zip a084126_list a084127_list,                       a070939 p == a070939 q] -- Reinhard Zumkeller, Nov 10 2013 CROSSREFS Cf. A078972, A007088, A070939, A055642. Cf. A084126, A084127, A070939. Cf. A138510, A174956. Cf. A261073, A261074, A261075 (subsequences). Intersection of A001358 and A266346. Sequence in context: A338309 A246569 A326063 * A190300 A338378 A081614 Adjacent sequences:  A085718 A085719 A085720 * A085722 A085723 A085724 KEYWORD nonn,base,look AUTHOR Reinhard Zumkeller, Jul 20 2003 EXTENSIONS Edited by Charles R Greathouse IV, Aug 02 2010 STATUS approved

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Last modified December 2 10:34 EST 2021. Contains 349437 sequences. (Running on oeis4.)