1989, Russian Mathematical Olympiad

Find the positive integers nn with exactly 1212 divisors 1=d1<d2<<d12=n1=d_1<d_2<\cdots<d_{12}=n such that the divisor with index d41d_4-1 (that is, dd41d_{d_4-1}) is (d1+d2+d4)d8(d_1+d_2+d_4)d_8.

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