[seqfan] number 999999000000

[Max Alekseyev]

SeqFans,

Quite amazingly, the number n = 999999000000 is the largest known n that is
divisible by ceiling(n^(1/k)) for all integer k>=1.
That is, it is the largest known element of http://oeis.org/A261206
There are no larger ones below 10^16 and it looks plausible that this
sequence is finite. Can anyone prove this?

(Or can the structure of 999999000000 suggest larger terms? I do not see
any connections here.)

Same question applies to the sister sequence  http://oeis.org/A261205

Regards,
Max