(-1)Sigma

[koh]

    Hi,Seqfans
    I submitted sequences related with (-1)Sigma.

   

    
    %I A000001
    %S A000001 6,140,312,1560,14384,18018,40992,2337400,7012200,11027016

    %N A000001 Numbers such that (-1)Sigma(m)*Sigma(m)= k*UnitaryPhi(m)*m, for some integer k.
    %C A000001 R.J.Mathar did an exhaustive search up to 30000000.
               Kohmoto found more terms.
    2^8*7*19*37*73*509, 2^8*5*7*19*37*509, 2^8*5^2*7*19*29*31*37*509, 2^9*3*11*31*1021, 2^9*3*7*11^2*19*31*131*1021, 2^11*3^6*5*7*13*23*137*467*1093*4093, 2^13*3*11*43*127*16381, 2^13*3*7*11^2*19*43*127*131*16381    
               But between 3*10^7 and them, many terms may lack.
               If both 2^n-3 and 2^n-1 are prime them numbers of the form 2^(n-1)*(M_n-2)*M_n appear on the sequence. Where M_n means Mersenne prime.     
    %Y A000001 A000002
    %K A000001 none
    %O A000001 1,1
    %A A000001 Yasutoshi Kohmoto   zbi74583 at boat.zero.ad.jp 



    %I A000002
    %S A000002 2,4,5,6,4,4,6,6,8,11
    %N A000002 Sequence gives k numbers of A000001
    %Y A000002 A000001
    %K A000002 none
    %O A000002 1,1
    %A A000002 Yasutsohi Kohmoto   zbi74583 at boat.zero.ad,jp 

   
    
    The case  that both 2^n-3 and 2^n-1 are prime exist only two n=3 and n=5.
    
    Is it provable   that they are all?
    Or, is there any possibility of third case?
    
    Yasutoshi