[seqfan] Re: UnitaryPhi

[zbi74583_boat at yahoo.co.jp]

    Hi  Seqfans

    b(n) : The smallest number  m  such that UnitarySigma(m) = n/(n-2)*m
    b(n) : 0, 6, 12, 2, 1080, 3, 56, 4, 2^5*3^3*5^2*7^2*13, 5, 2^6*3^4*5^3*7^2*11*41    OFFSET   3    If n=2*k then b(n)=a(k)  If n=2*k+1 and GCD(a(n),a(n-1))=1 then b(n)=a(n)*a(n-1)    ....  T.3  T.4
    Where a(n)=A14680(n)  The smallest number  m  such that UnitarySigma(m)=n/(n-1)*m    The case that n is odd and not(GCD(a(n),a(n-1))=1) is interesting problem
    I tried to prove the theorem          T.4.      Unexpectedly it is difficult    Could anyone prove it?


    Yasutoshi