Emmanuel Vantieghem sent the
following nice puzzle:
The last two weeks I used to browse
through my old notes. One of them could result in a "puzzle"
or a "problem" for your site.
It is about numbers of the
form (p^2)*Q, where Q is squarefree and p a prime
bigger than the greatest prime factor of Q.
Here are the first such numbers :
4, 9, 18, 25, 49, 50,
75, 98, 121, 147, 150, 169, 242, 245, 289, 294, 338, 361,
363, 490, ...
(A229027 at the OEIS)
I was mainly interested in consecutive integers of that
It was easy to find many
examples. These are the smallest ones :
I believe that there are
infinitely many of them. So, this can be the first question
there infinitely many consecutive numbers in A229027 ? (It
would already be fine if you can send huge numbers).
A more difficult question is
to find three consecutive integers of that form. There are
none below 2*10^10. So, this could give
Find three consecutive integers in that sequence or prove
that this is impossible.