[seqfan] Integers with a peculiar divisibility property

[Allan Wechsler]

Let sigma be the familiar sum-of-divisors function.

While hunting multiply perfect numbers, I learned that

sigma(19^4) = 151 * 911,

and sigma(151) and sigma(911) are both divisible by 19. This prompted me to
investigate which numbers n have sigma(sigma(n^4)) divisible by n^2.

I wrote a Haskell one-liner to list them -- but it computes sigma by brute
force, so it's very very slow. So far it has found:

1,2,4,8,16,19,21,25,32,38,42,50,57,64 ... which is not in OEIS.

The "primitive" elements (not products of smaller elements) are 2, 19, 25,
... and even this tiny three-element sequence is not in OEIS. Can anyone
whip up a faster program to look for bigger primitives?