Euler numbers (mod n^2)

[Hans Havermann]

> n such that the n-th Euler number == 1 (mod n^2)
> I get only :
> 2,17,37,.......

2, 17, 37, 1153, 1303, ...

> n such that the n-th Euler number == 1 (mod n)
> 2,3,4,5,7,8,11,13,15,16,17,19,23,29,31,32,37,41,43,47,53,59,61,64,67,71 
> ,73,79,83,89,91,97,....
> The first composites (not a power of 2)  are 15,91...

15, 91, 289, 319, 435, 561, 692, 703, 1016, 1105, 1369, 1495, 1729, ...