Amicable Pair/Examples/3^4 x 5 x 11 x 5281^19 x 29 x 89 (2 x 1291 x 5281^19 - 1)-3^4 x 5 x 11 x 5281^19 (2^3 x 3^3 x 5^2 x 1291 x 5281^19 - 1)

Example of Amicable Pair
These integers:
 * $3^4 \times 5 \times 11 \times 5281^{19} \times 29 \times 89 \paren {2 \times 1291 \times 5281^{19} - 1}$
 * $3^4 \times 5 \times 11 \times 5281^{19} \paren {2^3 \times 3^3 \times 5^2 \times 1291 \times 5281^{19} - 1}$

form an amicable pair.

Proof
By definition, $m$ and $n$ form an amicable pair :
 * $\map \sigma m = \map \sigma n = m + n$

where $\map \sigma n$ denotes the $\sigma$ function.

First it is established (by means of an online big integer calculator and integer factorisation calculator):
 * $2 \times 1291 \times 5281^{19} - 1$ is prime
 * $2^3 \times 3^3 \times 5^2 \times 1291 \times 5281^{19} - 1$ is prime

Thus from Sigma Function of Integer: Corollary:

Then we calculate the sum, by means of the same online big integer calculator and integer factorisation calculator: