MathDB

<span class='latex-bold'>N3:</span>

For any positive integer

n

, define

rad(n)

to be the product of all prime divisors of

n

(without multiplicities), and in particular

rad(1)=1

. Consider an infinite sequence of positive integers

\{a_n\}_{n=1}^{\infty}

satisfying that \begin{align*} a_{n+1} = a_n + rad(a_n), \: \forall n \in \mathbb{N} \end{align*} Show that there exist positive integers

t,s

such that

a_t

is the product of the

s

smallest primes. Proposed by ltf0501

Problem Statement