A073087(5)

[Lambert Klasen]

Dear seqfans,

ID Number: A073087
URL:       http://www.research.att.com/projects/OEIS?Anum=A073087
Sequence:  1,6,30,210
Name:      Least k such that sigma(k^k)>=n*k^k.

Comments:  Does a(n) = the product of primes less than or equal to
prime(n+1) A002110 (n+1)?


it is obvious, that A073087 is a subset of A002110.
define f(n) = sigma(n^n)/n^n, then the primorials
supply local maxima for f(n), which are not
exeeded in the interval [p#(n) .. p#(n+1)-1].
in fact there are prime(n+1)-1 equal terms
with offset p#(n).

example:
forstep(s=210,2310,210,r=sigma(s^s)/s^s*1.0;print(s," ",r))
210 4.375000000000000000000000000
420 4.375000000000000000000000000
630 4.375000000000000000000000000
840 4.375000000000000000000000000
1050 4.375000000000000000000000000
1260 4.375000000000000000000000000
1470 4.375000000000000000000000000
1680 4.375000000000000000000000000
1890 4.375000000000000000000000000
2100 4.375000000000000000000000000
2310 4.812500000000000000000000000

so the answer to the above question is no.
and the next term in the sequence a(5) is most likely 30030.

but i cannot compute a(5) due to lack of memory.
using PARI, it needs more then 1GB of memory which i unfortunately
do not possess.

anyone help ?


best regards
         Lambert

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