# [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 zbi74583.boat at orange.zero.jp
Mon Feb 2 06:05:14 CET 2009

```    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

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