In the triangular array below, n different prime numbers p_1, p_2, \dots, p_n are written in the bottom row. Then in each box, we write the product of the two numbers below it. The number $K = p_1^{\alpha_1} p_2^{\alpha_2} \dotsm p_n^{\alpha_n}$ is written in the box at the very top. If \alpha_2 = 2, then how many numbers in the array are divisible by the number p_4?

nathanl6656 Oct 30, 2024