[seqfan] Re: A007357 infinitary perfect number b-file

[Vladimir Shevelev]

Maybe, it is interesting that these numbers I introduced in 1983 by the name "Garmonic numbers" in a note "Factorization with distinct factors", Kvant, no. 5 (1983) p.37 (in Russian) (now Kvant there is On-Line) with calculating by handy the first 4 such numbers. Further, in a large paper "Multiplicative
functions in the Fermi-Dirac arithmetic", Izv. VUZov Sev.-Kav. Reg. Est. Nauki. no.4 (1996), 28-43  (in Russian) (see large review in MR: 2000f:11097), I published a list of all 36 such numbers up to 2^16 by name "Fermi-Dirac perfect numbers". A remarkable programmer V.M. Ermakov helped me in that using SMALLTALK,v.2. Unfortunately, he died in 1996. Later, already in Israel, S. Litsyn
( with whom we worked on a general paper "On factorization of integers with restrictions on the exponents", INTEGERS, no.7 (2007), #A33, 1-35) told me about OEIS and I wanted to submit
this sequence, but we found these numbers by the third name "Infinitary perfect numbers." In that time I learned about paper by G.L. Cohen "On an integer's infinitary divisors, Math. Comput. 54, (1990), 395-411. The  notion "infinitary divisors" was quite new for me. Further,
we found these name in Wolfram MathWorld, and I learned that J. M. Pedersen in "Tables of Aliquot Cycles." http://amicable.adsl.dk/aliquot/infper.txt. " in 2004 calculated the first 155 iperfect numbers.
 
Regards,
Vladimir

----- Original Message -----
From: Richard Mathar <mathar at strw.leidenuniv.nl>
Date: Friday, March 18, 2011 21:43
Subject: [seqfan] A007357 infinitary perfect number b-file
To: seqfan at seqfan.eu

> 
> Does anyone known whether the list in A007357, the infinitary 
> perfect numbers
> with isigma(n) =2*n, can be extended by just copying a list of known
> infinitary perfect numbers from 
> http://amicable.adsl.dk/aliquot/i1/i1.txtinto a b-file? That is, 
> does http://amicable.adsl.dk/aliquot/i1/i1.txt
> contain holes?
> 
> Richard
> 
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 Shevelev Vladimir‎