Giuga Number/Examples/244,197,000,982,499,715,087,866,346

Example of Giuga Number
$244 \, 197 \, 000 \, 982 \, 499 \, 715 \, 087 \, 866 \, 346$ is a Giuga number:
 * $\dfrac 1 2 + \dfrac 1 3 + \dfrac 1 {11} + \dfrac 1 {23} + \dfrac 1 {31} + \dfrac 1 {47 \, 137} + \dfrac 1 {28 \, 282 \, 147} + \dfrac 1 {3 \, 892 \, 535 \, 183} - \dfrac 1 {244 \, 197 \, 000 \, 982 \, 499 \, 715 \, 087 \, 866 \, 346} = 1$

Proof
We have that:
 * $244 \, 197 \, 000 \, 982 \, 499 \, 715 \, 087 \, 866 \, 346 = 2 \times 3 \times 11 \times 23 \times 31 \times 47 \, 137 \times 28 \, 282 \, 147 \times 3 \, 892 \, 535 \, 183$

Then we have:

Adding all these up together:

Dividing both sides by $244 \, 197 \, 000 \, 982 \, 499 \, 715 \, 087 \, 866 \, 347$ makes the result apparent by definition of Giuga number.