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Find all positive integers

Source: Baltic way 2005/20

November 8, 2005
number theory proposednumber theory

Problem Statement

Find all positive integers n=p1p2⋯pkn=p_1p_2 \cdots p_k which divide (p1+1)(p2+1)⋯(pk+1)(p_1+1)(p_2+1)\cdots (p_k+1) where p1p2⋯pkp_1 p_2 \cdots p_k is the factorization of nn into prime factors (not necessarily all distinct).
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