COMMENT on A113791.

[koh]

    Neil, Bob.

    The definition of "1/m-Sociable number of order k" is described on this page.

    http://mathworld.wolfram.com/SociableNumbers.html

    And the following theorem is proved.
    "If M_m and M_n are distinct Mersenne primes then {2^(m-1)*M_n, 2^(n-1)*M_m} is 1/2-Sociable number of order 2."

    To Eric.
    In the proof on this page, a typo mistake exists.

    mistake          correct
    2(n-1)           2^(n-1)
   
    Yasutoshi


>Neil,
>
>	I took out a space in the title, added the Mathematica coding, extended the
>sequence and took out the 'more'. I left in the 'uned' since I am not sure of
>that part of the title "1/2-Sociable number of order 1 or 2".
>
>Thanx, Bob.
>
>
>%I A113791
>%S A113791 6,12,14,28,48,62,112,124,160,189,192,254,448,496,508,1984,2032,8128,
>%T A113791 12288,16382,28672,32764,126976,131056,196608,262142,458752,520192,
>%U A113791 524224,524284,786432,1048574,1835008,2031616,2097136,2097148,8126464
>%N A113791 Let S(n)=1/2*Sigma(n). Numbers such that S(S(n))=n, 1/2-Sociable number of order 1 or 2.
>%C A113791 Almost all terms are of the form that 2^m*M_k .Where M_k means Mersenne prime 2^k-1. a(9)=2^5*5 and a(10)=3^3*7 are sporadic solutions. S(a(9))=a(10).
>%H A113791 <a href="http://mathworld.wolfram.com/SociableNumbers.html">WathWorld</a>
>%t A113791 Select[ Range at 8323071, DivisorSigma[1, DivisorSigma[1, #]/2] == 2# &] (* RGWv *)
>%K A113791 none,uned
>%O A113791 1,1
>%A A113791 Yasutsohi Kohmoto zbi74583(AT)boat.zero.ad,jp
>%E A113791 More terms from RGWv (rgwv(at)rgwv.com), Jan 21 2006
>
>P.S. The sequence continues: 8323072, 8388544, 8388592, 33292288, 33550336, 33554368, (10^8)
>