Divide Sum of Divisors

Level pending

Let $A$ be the sum of all divisors of $2^{18}+1$ .

What is the value of $[\frac{A}{1000}]$ ?

( $[x]$ is the greatest integer function )

1 solution

Joe Mansley
Apr 16, 2021

$2^{18}+1 = (2^6+1)(2^{12}-2^6+1) = 65 \times 4033$

$4033 = 37 \times 109$ (I don't know a fast way to find these factors. I just checked divisibility by 3,5,7,...)

So $2^{18}+1=5 \times 13\times 37\times 109$

So $A=(1+5)(1+13)(1+37)(1+109) = 351120$