MathDB

Let

a_1, a_2, a_3, \ldots

a sequence of positive integers that satisfy the following conditions:

a_1=1, a_{n+1}=a_n+a_{\lfloor \sqrt{n} \rfloor}, \forall n\ge 1

Prove that for every positive integer

k

there exists a term

a_i

that is divisible by

k

P6