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Interoceanic numbers

Source: Centroamerican 2020, problem 6

October 28, 2020
number theoryprime factorization

Problem Statement

A positive integer NN is interoceanic if its prime factorization
N=p1x1p2x2⋯pkxkN=p_1^{x_1}p_2^{x_2}\cdots p_k^{x_k}
satisfies
x1+x2+⋯+xk=p1+p2+⋯+pk.x_1+x_2+\dots +x_k=p_1+p_2+\cdots +p_k.
Find all interoceanic numbers less than 2020.
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