d(sigma(n)) = sigma(d(n))

[Dean Hickerson]

Leroy Quet wrote:

> Is the sequence of n's such that d(sigma(n)) = sigma(d(n)) in the EIS?

Yes, it's A076361.

> Is this sequence infinite?

Yes, assuming that Schinzel's hypothesis is true.  See:

    http://mathworld.wolfram.com/SchinzelsHypothesis.html

That conjecture implies that there are infinitely many primes p for which
(p^2+p+1)/3  is prime.  (E.g. p = 7, 13, 19, 31, 43, 73, 97, ...)  For such
p, we have  d(sigma(p^2)) = d(p^2+p+1) = 4  and  sigma(d(p^2)) = sigma(3) = 4,
so p^2 is in the sequence.

Dean Hickerson
dean at math.ucdavis.edu