1,1

These are the first terms of A023196, A107912, A107913, A107914. - Jud McCranie (j.mccranie(AT)comcast.net), May 28 2005

a(5) > 4*10^9 - if it exists. - Jud McCranie (j.mccranie(AT)comcast.net), 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

sigma(sigma(sigma(9)))=24 >= 2*9, so a(3)=9.

Cf. A000203, A055020, A107912-A107914, A060800.

Sequence in context: A142871 A050235 A018801 this_sequence A141379 A100616 A097474

Adjacent sequences: A055018 A055019 A055020 this_sequence A055022 A055023 A055024

fini,full,nonn

Jud McCranie (j.mccranie(AT)comcast.net), May 31 2000