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Elements in S such that difference of divisors is 22

Source: French TST 2002

June 17, 2011
number theory proposednumber theory

Problem Statement

Consider the set SS of integers kk which are products of four distinct primes. Such an integer k=p1p2p3p4k=p_1p_2p_3p_4 has 1616 positive divisors 1=d1<d2<…<d15<d16=k1=d_1<d_2<\ldots <d_{15}<d_{16}=k. Find all elements of SS less than 20022002 such that d9−d8=22d_9-d_8=22.
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