Extending A075880, how to find n for A001481(n)=x for large x

[Pfoertner, Hugo]

Is there a clever technique to find n in A001481(n)=x (the list of all
numbers expressable as the sum of 2 squares) for a given (large) term x of
this sequence? To create A075880(n) = k such that A001481(k) = A071383(n) I
used brute force, i.e. creating all sums of squares up to some given limit,
sorting and counting.

If a better technique exists, can someone compute the column k in the
following table:


A001481(k)  k
5          4
25         13
....
148208125  27044791
243061325  ? (I got 39544748, probably wrong?)
1215306625 ?
3159797225 ?
6076533125 ?
12882250225 ?
53716552825 ?
64411251125 ?   the last term of A071383 given in EIS
if you want to continue ...
167469252925
322056255625
785817263725
2846977299725
3929086318625
10215624428425
19645431593125
51078122142125
173665615283225
255390610710625
286823301259625
745740583275025
1434116506298125
3728702916375125
12677589915675425
18643514581875625
25527273812106625
63387949578377125
127636369060533125
316939747891885625
331854559557386125
1128305502495112825
1659272797786930625
2476145559774342625
5641527512475564125   (the squared radius of the smallest circle around
(0,0) hitting 18432 lattice points)

Thanks

Hugo Pfoertner