(-1)Sigma,Sigma,UnitarySigma,UnitaryPhi

[koh]

    Dear Guy and Seqfans.

    These two farther generalizations of perfect number are interesting so I think they may fit to UPINT4, if will be published.

    (-1)Sigma(m)*Sigma(m)/UnitaryPhi(m)=k*m             ....E_1
    (-1)Sigma(m)*UnitarySigma(m)/UnitaryPhi(m)=k*m      ....E_2
    

    S_1 : 2*3, 2^2*5*7, 2^3*3*13, 2^3*3*5*13, 2^4*29*31, 2^5*3*7*61, 2^8*7*19*37*73*509, 2^8*5*7*19*37*509, 2^9*3*11*31*1021, 2^11*3^6*5*7*13*23*137*467*1093*4093
           K= 2,4,5,6,4,6,5,6,6,7

    S_2 : 2*3, 2^3*3*13, 2^4*3*17*29, 2^5*3*11*61, 2^8*3*11*43*257*509  

           K= 2,3,3,3,3

    I have not done a exhaustive search.
    I wish someone will do it.

    Yasutoshi