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A(n) divides B(n)

Source: 2023 Israel TST Test 3 P2

March 23, 2023
TSTnumber theoryDivisors

Problem Statement

For each positive integer nn, define A(n)A(n) to be the sum of its divisors, and B(n)B(n) to be the sum of products of pairs of its divisors. For example, A(10)=1+2+5+10=18A(10)=1+2+5+10=18 B(10)=1⋅2+1⋅5+1⋅10+2⋅5+2⋅10+5⋅10=97B(10)=1\cdot 2+1\cdot 5+1\cdot 10+2\cdot 5+2\cdot 10+5\cdot 10=97 Find all positive integers nn for which A(n)A(n) divides B(n)B(n).
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