title: 数列用表示正整数的最大奇因子，如g(3)=3,g(10)=5,( 
desc: 用表示正整数的最大奇因子，如g(3)=3,g(10)=5,(1)求g(100),(2)求g(1)+g(2)+g(3)+.....+g(2^n)的简缩公式
answer: (1)求g(100)=25
  
  (2)
  1.g(2k+1)=2k+1
  
  2.g(2k)=g(k)
  
  3.An=g(1)+g(2)+g(3)+.....+g(2^n)
  ==>
  An=[g(1)+g(3)+.....+g(2^n-1)]+
  +[g(2)+g(4)+.....+g(2^n)]=
  =[1+3+.....+2^n-1]+[g(1)+g(2)+.....+g(2^(n-1))]=
  =2^(2n-2)+A(n-1)=
  =2^(2n-2)+2^(2n-4)+A(n-2)=
  =2^(2n-2)+2^(2n-4)+..+2^2+A(1)=
  =2^(2n-2)+2^(2n-4)+..+2^2+2=
  =[4^n-1]/3+1
  ==>
  g(1)+g(2)+g(3)+.....+g(2^n)=[4^n-1]/3+1
  