
COMMENTS

These are the first terms of A023196, A107912, A107913, A107914.  Jud McCranie, May 28 2005
a(5) > 4*10^9, if it exists.  Jud McCranie, May 28 2005
There are no more terms: sigma(2n) is never prime, so an even number needs at most two steps; sigma(n) is odd iff n is a square or twice a square. So A107914 (four recursive steps) contains only odd squares. Assume p prime so sigma(p^2) = p^2 + p + 1 = m^2 never meets the condition with p + 2k = m that (p + 2k)^2 = m^2. This implies the impossibility of a solution for numbers of the form p^(2i) and numbers of the form p^(2i)q^(2i).  Lambert Klasen (Lambert.Klasen(AT)gmx.net), Jun 06 2005
