On the products (1l+1) (2l+1) ... (nl+1), II

Text. In this paper, the following results are proved: (i) For any odd integer l with at most two distinct prime factors and any positive integer n, the product (1(l) + 1) (2(l) + 1)...(n(l) + 1) is not a powerful number; (ii) For any integer r >= 1, there exists a positive integer T-r such that, if l is a positive odd integer with at most r distinct prime factors and n is an integer with n >= T-r, then (1(l) + 1) (2(l) + 1)...(n(l) + 1) is not a powerful number. (C) 2014 Elsevier Inc. All rights reserved.