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 A192734 Smallest number having binary weight of 3 and n distinct prime factors 1

%I

%S 7,21,273,16401,1048593,4295032833,1099512676353,9007199256838145,

%T 302231455185132270387201,1208944266358702884257793,

%U 1329227995784915872903807060297121793,1393796574908163946347162983661240005427201

%N Smallest number having binary weight of 3 and n distinct prime factors

%C Written in binary, these numbers have exactly three 1 bits and the other bits are all 0's. This means that these numbers are of the sum of 1 plus two larger distinct powers of 2. - _Alonso del Arte_, Jul 08 2011

%C a(n) > A002110(n). [_Reinhard Zumkeller_, Jul 09 2011]

%C Sequence is not monotone: a(12) > a(13). [_Charles R Greathouse IV_, Jul 11 2011]

%H Charles R Greathouse IV, <a href="/A192734/b192734.txt">Table of n, a(n) for n = 1..14</a>

%t list = {7}; For[max = 1; n = 2, n < 120,

%t For[m = 0, m < n,

%t tal = 2*(2^n + 2^m) + 1; num = PrimeNu[tal];

%t If[num > max, AppendTo[list, tal]; max = num]

%t , m++], n++] (* Sarnbratt *)

%t A084468 = Flatten[Table[2^m + 2^n + 1, {m, 2, 80}, {n, m - 1}]]; Flatten[Table[Take[Select[A084468, PrimeNu[#] == n &], 1], {n, 10}]] (* _Alonso del Arte_, Jul 08 2011 *)

%o (PARI) a(n)={

%o my(t);

%o for(a=2,9e9,

%o t=1+1<<a;

%o for(b=1,a-1,

%o if(omega(t+1<<b)==n,return(t+1<<b))

%o )

%o )

%o }; \\ _Charles R Greathouse IV_, Jul 08 2011

%o a192734 n = head [x | x <- [2^u + 2^v + 1 | u <- [2..], v <- [1..u-1]],

%o a001221 x == n]

%o -- _Reinhard Zumkeller_, Jun 14 2015, Jul 09 2011

%Y Cf. A084468, A001221.

%K nonn,base

%O 1,1

%A _Johan SĂ¤rnbratt_, Jul 08 2011

%E a(9) corrected by _Charles R Greathouse IV_, Jul 08 2011

%E a(12) from _Charles R Greathouse IV_, Jul 11 2011

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Last modified July 29 12:47 EDT 2021. Contains 346346 sequences. (Running on oeis4.)