# [seqfan] Re: Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v

Richard Guy rkg at cpsc.ucalgary.ca
Mon Nov 24 23:10:45 CET 2008

```In connexion with A125490,1,2, I sh'd've
pointed out further that the interesting
thing is that

sigma(x) = sigma(y) = sigma(z) [=x+y+z]

where the contents of the bracket are
not mentioned.  Is the sequence of  x+y+z
in OEIS?  It starts 6552, 30240, ...  R.

On Sun, 23 Nov 2008, Richard Guy wrote:

> Neil & others,
>              This discovery prompted me to look
> up
> amicable triples & quadruples in OEIS.  For the
> former,
> I found x, y, z, in A125490,1,2, but didn't find
> x+y+z.
>
>              For the latter, there's some
> confusion,
> A036471,2,3,4  shd be a,b,c,d and A116148
> a+b+c+d,
> but there seems to be something wrong with the
> statements.
>
>              Best to all,   R.
>
> On Sun, 23 Nov 2008, koh wrote:
>
>>     Dear Seqfans
>>
>>     I submitted Amicable 5-ple sequence.
>>     It is the first known example.
>>     More term  are wanted.
>>
>>
>>
>> % I A000001
>> % S A000001 227491164588441600
>> % N A000001 5-ple x,y,z,u,v such that
>> % Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v
>>                Sequence gives the smallest
>>     element.
>> % C A000001 Resta computed up to 10^7, but no
>> % example exists.
>> % Y A000001 A000002,A000003,A000004,A000005
>> % K A000001 none
>> % O A000001 1,1
>> % A A000001 Yasutoshi Kohmoto
>> % zbi74583.boat at orange.zero.jp
>>
>>
>> % I A000002
>> % S A000002 228507506351308800
>> % N A000002 5-ple x,y,z,u,v such that
>> % Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v
>>                Sequence gives second smaller
>>     element.
>> % Y A000002 A000001,A000003,A000004,A000005
>> % K A000002 none
>> % O A000002 1,1
>> % A A000002 Yasutoshi Kohmoto
>> % zbi74583.boat at orange.zero.jp
>>
>>
>> % I A000003
>> % S A000003 229862628701798400
>> % N A000003 5-ple x,y,z,u,v such that
>> % Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v
>>                Sequence gives 3rd smaller
>>     element.
>> % Y A000003 A000001,A000002,A000004,A000005
>> % K A000003 none
>> % O A000003 1,1
>> % A A000003 Yasutoshi Kohmoto
>> % zbi74583.boat at orange.zero.jp
>>
>>
>> % I A000004
>> % S A000004 230878970464665600
>> % N A000004 5-ple x,y,z,u,v such that
>> % Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v
>>                Sequence gives 4th smaller
>>     element.
>> % Y A000004 A000001,A000002,A000003,A000005
>> % K A000004 none
>> % O A000004 1,1
>> % A A000004 Yasutoshi Kohmoto
>> % zbi74583.boat at orange.zero.jp
>>
>>
>> % I A000005
>> % S A000005 243752632794316800
>> % N A000005 5-ple x,y,z,u,v such that
>> % Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v
>>                Sequence gives the largest
>>     element.
>> % Y A000005 A000001,A000002,A000003,A000004
>> % K A000005 none
>> % O A000005 1,1
>> % A A000005 Yasutoshi Kohmoto
>> % zbi74583.boat at orange.zero.jp
>>
>>
>>
>>     Yasutoshi
>>
>>
>>
>>  _______________________________________________
>>
>>  Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
>>
>

```