[seqfan] UnitarySigma(x) = UnitarySigma(y) = UnitarySigma(z) = 3*(x*y*z)^(1/2)/(- x^(1/2) + 8*y^(1/2) ? 5*z^(1/2))

[zbi74583.boat at orange.zero.jp]

    Hi, Seqfans
    I considered the following numbers.

         UnitarySigma(x) = UnitarySigma(y) = UnitarySigma(z) =
3*(x*y*z)^(1/2)/(- x^(1/2) + 8*y^(1/2) ? 5*z^(1/2)) , z<=y<=x



    %I A000001
    %S A000001 2, 20, 24,, 360, 816, 1056, 12240, 15840, 29120, 181632, 337977,
2724480, 93358848, 1400382720
    %N A000001 Numbers x,y,z such that UnitarySigma(x) = UnitarySigma(y) =
UnitarySigma(z) = 3*(x*y*z)^(1/2)/(- x^(1/2) + 8*y^(1/2) ? 5*z^(1/2)) ,
z<=y<=x
               Sequence gives x.
    %C A000001 a(11) is the smallest term for x!=y, y!=z, x!=z
               If x=y=z then it becomes ?multiply unitary prefect number? such
that UnitariSigma(x)=3/2:x .
   %e A000001 Factorization of a(11) :
               17*3^2*47^2
    %Y A000001 A000002, A000003
    %K A000001 none
    %O A000001 0,1
    %A A000001 Yasutoshi Kohmoto zbi74583.boat at orange.zero.jp

    %I A000002
    %S A000002 2, 20, 24,, 360, 816, 1056, 12240, 15840, 29120, 181632, 333200,
2724480, 93358848, 1400382720
    %N A000002 Numbers x,y,z such that UnitarySigma(x) = UnitarySigma(y) =
UnitarySigma(z) = 3*(x*y*z)^(1/2)/(- x^(1/2) + 8*y^(1/2) ? 5*z^(1/2)) ,
z<=y<=x
               Sequence gives y
    %e A000002 Factorization of a(11) :
                17*5^2*2^4*7^2
    %Y A000002 A000001, A000003
    %K A000002 none
    %O A000002 0,1
    %A A000002 Yasutoshi Kohmoto zbi74583.boat at orange.zero.jp

%I A000003
    %S A000003 2, 20, 24,, 360, 816, 1056, 12240, 15840, 29120, 181632, 287300,
2724480, 93358848, 1400382720
    %N A000003 Numbers x,y,z such that UnitarySigma(x) = UnitarySigma(y) =
UnitarySigma(z) = 3*(x*y*z)^(1/2)/(- x^(1/2) + 8*y^(1/2) ? 5*z^(1/2)) ,
z<=y<=x
               Sequence gives z.
    %e A000003 Factorization of a(11) :
               17*5^2*2^2*13^2
    %Y A000003 A000001, A000002
    %K A000003 none
    %O A000003 0,1
    %A A000003 Yasutoshi Kohmoto zbi74583.boat at orange.zero.jp