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A192734
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Smallest number having binary weight of 3 and n distinct prime factors
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1
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7, 21, 273, 16401, 1048593, 4295032833, 1099512676353, 9007199256838145, 302231455185132270387201, 1208944266358702884257793, 1329227995784915872903807060297121793, 1393796574908163946347162983661240005427201
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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MATHEMATICA
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list = {7}; For[max = 1; n = 2, n < 120,
For[m = 0, m < n,
tal = 2*(2^n + 2^m) + 1; num = PrimeNu[tal];
If[num > max, AppendTo[list, tal]; max = num]
, m++], n++] (* Sarnbratt *)
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 *)
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PROG
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(PARI) a(n)={
my(t);
for(a=2, 9e9,
t=1+1<<a;
for(b=1, a-1,
if(omega(t+1<<b)==n, return(t+1<<b))
)
)
(Haskell)
a192734 n = head [x | x <- [2^u + 2^v + 1 | u <- [2..], v <- [1..u-1]],
a001221 x == n]
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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