[seqfan] Re: Asymptotic for A074753

[Richard Mathar]

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:

read("transforms3") ;
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) ;