Let $n,d$ be natural numbers. Prove that there is an arithmetic sequence of positive integers. $$a_1,a_2,...,a_n$$with common difference of $d$ and $a_i$ with prime factor greater than or equal to $i$ for all values $i=1,2,...,n$. (nooonuii)
Problem
Source: Mathcenter Contest / Oly - Thai Forum 2008 R3 p7 https://artofproblemsolving.com/community/c3196914_mathcenter_contest
Tags: arithmetic sequence, number theory