A085721 - OEIS

A085721

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

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).