OFFSET
2,1
COMMENTS
That is, the amicable pair is (2^n pq, 2^n rs) for odd primes p, q, r, s. See A180331 for the numbers 2^n rs. It is easy to show that the four primes must satisfy the equation (p+1)(q+1) = (r+1)(s+1). These amicable pairs are a subset of the regular type (2,2) pairs, which are cataloged by Pedersen. These amicable pairs can be found by using Herman te Riele's method 2. Amicable pairs of this form are known for 1 < n < 49. Do they exist for all n?
LINKS
J. M. Pedersen, Regular type (2,2) amicable pairs
Herman J. J. te Riele, On generating new amicable pairs from given amicable pairs, Math. Comp. 42 (1984), 219-223.
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Sep 07 2010
STATUS
approved