[seqfan] [math-fun] Forwarded mail.... (fwd)

[Richard Guy]

This message was kicked back.  Trying again.  R.

---------- Forwarded message ----------
Date: Mon, 6 Jul 2009 08:44:36 -0600 (MDT)
From: Richard Guy <rkg at cpsc.ucalgary.ca>
Reply-To: math-fun <math-fun at mailman.xmission.com>
To: Sequence Fans <seqfan at ext.jussieu.fr>
Cc: Math Fun <math-fun at mailman.xmission.com>
Subject: [math-fun] Forwarded mail....

For info on the behavior of aliquot
sequences, see

Richard K.~Guy \& J.~L.~Selfridge, What drives an 
aliquot
   sequence? {\it Math.\ Comput.}, {\bf 29}(1975)
   101--107;
   {\it MR} {\bf 52} \#5542.

For the latest I have on 46758 or 99225
[assuming I've made no errors] see the
following, where  %x  shoud be read as

   s^{758+x)(99225) = s^{759+x}(46758}

and  s(n) = sigma(n) - n.

The max so far is  x = 10  with 109 decimal
digits.  It is presently equipped with a
down-dribbler,  2^2 without 7.  x = 18
will have only 108 digits.  What are  p
and  q ?

%10 = 
2634352957536601215651504310367034664237525994841454140912074056001634101746270450889034819192963235153851324
? sigma(%10)-%10
%11 = 
4375257663618965969838703886908135210362400648826184831403998005722029284842736914906603629552172468620027076
? sigma(%11)-%11
%12 = 
3812107258892467560724974268427776342559095577235276386026267812986314208130577642999593014216712259224932924
? sigma(%12)-%12
%13 = 
3357281129948365843366244433222476932983757953562658831902107291213172363666597435003856377831158249456856516
? sigma(%13)-%13
%14 = 
2518171581657269542751815956477757174750853819031465204680695087344865157789907955347820287620116570491943484
? sigma(%14)-%14
%15 = 
1888629123883173758068189431062891256470513916997092605609774658685559002236728244577771226723234026392998116
? sigma(%15)-%15
%16 = 
1416471844370396313297145002601020142112938329621791431806267389982998189766074091264106125133452654937155868
? sigma(%16)-%16
%17 = 
1062353883280402701838073792504970617432775483305445625911321617689753946299262182125924369941690102569916132
[= 
2^2*15178595752127*230389769006487808825024129*p*q]

R.



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