# [seqfan] Re: Asymptotic for A074753

Christopher Gribble chris.eveswell at virgin.net
Fri Jan 15 21:59:18 CET 2010

```Thanks very much Richard.

Chris

-----Original Message-----
From: seqfan-bounces at list.seqfan.eu [mailto:seqfan-bounces at list.seqfan.eu]
On Behalf Of Richard Mathar
Sent: 15 January 2010 8:48 PM
To: seqfan at seqfan.eu
Subject: [seqfan] Re: Asymptotic for A074753

On the limiting sequences of
http://list.seqfan.eu/pipermail/seqfan/2010-January/003486.html :

cg> I have been following this thread with interest and would like to
cg> suggest the two following sequences:
cg>
cg>   The smallest and largest values of n for which sigma(n) = A002191(n).
cg>
cg> I don't know whether they are in the OEIS or not but cannot find any
cg> indication that that they are.

The minimum (lower bound) function is in A002192. The maximum function (the
other
inverse), max(k) : sigma(k) = A002191(n), seems to be

1, 2, 3, 5, 4, 7, 11, 9, 13, 8, 17, 19, 23, 12, 29, 25, 31, 22, 37, 18, 27,
41,
43, 47, 53, 39, 49, 59, 61, 32, 67, 71, 73, 45, 79, 83, 89, 36, 50, 77,
97,
101, 103, 107, 109, 91, 113, 95, 81, 75, 82, 64, 127, 131, 121, 137,
139,
119, 149, 151, 125, 157, 133, 106, 163, 167, 98, 173, 129, 179, 181,
169,
122, 191, 193, 72, 197, 199, 134, 116, 211, 187, 100, 146, 223

and not yet in the OEIS. (Where A002191(n)='prime'+1, it shows just
'prime'.) In Maple:

a2191 := BFILETOLIST("b002191.txt") ;
A := proc(n,domin)
global a2191 ;
if domin then
for a from 1 do
if numtheory[sigma](a) = op(n,a2191) then
return a ;
end if;
end do ;
else
for a from op(n,a2191) by -1 do
if numtheory[sigma](a) = op(n,a2191) then
return a ;
end if;
end do ;
end if;
end proc:
seq(A(n,true),n=1..100) ;
seq(A(n,false),n=1..100) ;

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