MathDB

Determine if there exists an infinite sequence of not necessarily distinct positive integers

a_1, a_2, a_3,\ldots

such that for any positive integers

m

and

n

where

1 \leq m < n

, the number

a_{m+1} + a_{m+2} + \ldots + a_{n}

is not divisible by

a_1 + a_2 + \ldots + a_m

5