+36 In the triangular array below, different prime numbers p1, p2, .... pn are written in the bottom row. Then in each box, we write the product of the two numbers below it. The number K=p1^a1,p2^a2,pn^an is written in the box at the very top. If a2=8 then how many numbers in the array are divisible by the number p4?
unitsize(0.6 cm);
path box = (0,0)--(2,0)--(2,1)--(0,1)--cycle;
draw(box);
draw(shift((2,0))*(box));
draw(shift((4,0))*(box));
draw(shift((10,0))*(box));
draw(shift((12,0))*(box));
draw(shift((1,1))*(box));
draw(shift((3,1))*(box));
draw(shift((11,1))*(box));
draw(shift((5,5))*(box));
draw(shift((7,5))*(box));
draw(shift((6,6))*(box));
label("$\dots$", (8,0.5));
label("$\vdots$", (7,3.5));
label("$p_1$", (1,0.5), fontsize(10));
label("$p_2$", (3,0.5), fontsize(10));
label("$p_3$", (5,0.5), fontsize(10));
label("$p_{n - 1}$", (11,0.5), fontsize(10));
label("$p_n$", (13,0.5), fontsize(10));
label("$p_1 p_2$", (2,1.5), fontsize(10));
label("$p_2 p_3$", (4,1.5), fontsize(10));
label("$p_{n - 1} p_n$", (12,1.5), fontsize(10));
label("$K$", (7,6.5), fontsize(10));
[/asy]
