--- In primenumbers@y..., Phil Carmody <fatphil@a...> wrote:
> In other words, given non-square n, what's the size of the smallest
b that is a square-denier (yes, neologism) for n.
>
> Is there a case where the smallest square-denier for n is >sqrt(n)
(done without taking a square root, of course!)
> In Marcel's case the smallest square denier is b=2^2, for reference.
>

Cases of non-square n with smallest square-denier > sqrt(n):

n square-denier(n)
---------------------
2 3
3 4
5 3
6 4
7 4
8 3
10 4
12 5
13 5
15 4
21 8
24 7
40 7
45 7
60 9

This is likely a complete list. There are no others < 10^7.

Other numbers which are "record-setters" as the smallest n
with a particular square-denier:

n square-denier(n)
---------------------
184 11
280 13
364 16
1456 17
3124 19
5236 23
17185 25
25249 29
49504 37
233776 41
364144 43
775369 47
3864169 53
8794864 61

So, in some sense, these numbers could be considered pseudo-squares?