Multiamicable Numbers

Two integers  and  are -multiamicable if

and

where  is the divisor function and  are positive integers. If ,  is an amicable pair.

 cannot have just one distinct prime factor, and if it has precisely two distinct prime factors, then  and  is even. Small multiamicable numbers for small  are given by Cohen et al. (1995). Several of these numbers are reproduced in the table below.

1	6	76455288	183102192
1	7	52920	152280
1	7	16225560	40580280
1	7	90863136	227249568
1	7	16225560	40580280
1	7	70821324288	177124806144
1	7	199615613902848	499240550375424

REFERENCES:

Cohen, G. L; Gretton, S.; and Hagis, P. Jr. "Multiamicable Numbers." Math. Comput. 64, 1743-1753, 1995.ش