cp's OEIS Frontend

The numbers x and y form a WGM-amicable pair (WGM = Weighted Geometric Mean). See Dimitrov link. An amicable pair forms a WGM-amicable pair, so the larger member of an amicable pair A002046 is a term of this sequence. A check for x < y < 2*10^6 shows that all solutions (x,y) to the Diophantine equation sigma(x)^x * sigma(y)^y = (x+y)^(x+y) are amicable pairs. Although we cannot set an example, we cannot rule out the existence of WGM-amicable pairs that are not amicable pairs.

It is important to note that the brute-force search should be performed on the logarithmic form of the equation: x*log(sigma(x)) + y*log(sigma(y)) = (x+y) * log(x+y).

The numbers x, y and z form a GM-amicable triple (GM = Geometric Mean). See Dimitrov link. An amicable triple forms a GM-amicable triple, so the larger member of an amicable triple A125492 is a term of this sequence.