(-1)Sigma,Sigma,UnitarySigma,UnitaryPhi

[kohmoto]

    Hi, Richard.

    Thanks for your calculation of S_2.
    I will submit it to OES.

    Yasutoshi

    PS
    I know a famous researcher of Amicable Number, te Riele, who is a dutch 
mathematician.
    Do you know him?


----- Original Message ----- 
From: "Richard Mathar" <mathar at strw.leidenuniv.nl>
To: <seqfan at ext.jussieu.fr>
Sent: Monday, October 02, 2006 6:26 AM
Subject: Re: (-1)Sigma,Sigma,UnitarySigma,UnitaryPhi


>
>> From seqfan-owner at ext.jussieu.fr  Wed Sep 27 07:19:46 2006
>> Date: Wed, 27 Sep 2006 14:02:33 +0900
>> Subject: (-1)Sigma,Sigma,UnitarySigma,UnitaryPhi
>> From: "koh" <zbi74583 at boat.zero.ad.jp>
>> To: seqfan at ext.jussieu.fr
>>
>>     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
>
> S_2 (also named E_2 above) starts as
>
> n=6 (k=2)
> n=312 (k=3)
> n=495 (k=2)
> n=990 (k=3)
> n=20520 (k=4)
> n=23664 (k=3)
> n=64416 (k=3)
> n=13063050 (k=4)
>
> and there are no more terms smaller than n=74000000.
>
> RJ Mathar, http://www.strw.leidenuniv.nl/~mathar
>