report on recent OEIS activity / Bernoulli divisible by square

[Hans Havermann]

> Bernoulli B(2n) is divisible in a nontrivial way by a square."
> My example, found yesterday, is that the numerator of B_284 is 
> divisible by 37^2.

Just to get the ball rolling on this... If I take nontriviality as n 
being squarefree, some solutions are:

   n    ^2

  114  103
  142   37
  457   59
  717  271
1258   37
1298   59
1441  131
1474   37
1646   67
1943   67
2590   37
2806   37
2830  283
3009   59
3151  157

However, if the point was to catch *all* irregular primes, it fails for:

  592   37
  808   37
1236  103
1369   37
1924   37
2140   37
2168   59
2738   37
2884  101

So, some other definition of nontriviality?