P-k-x-N-n-N-x-gt-0-n-x-1-k-C-k-3-P-k-0-1-C-P-N-proof-or-give-a-counter-example-that-x-y-z-C-3-x-2-yz-x-y-x-z-

Question Number 1776 by 123456 last updated on 20/Sep/15

P_{k} = {x \in N, n \in N : x > 0, \sum_{n ∣ x} 1 = k}

C = \underset{k ⩾ 3}{\cup} P_{k}

{0, 1} \cup C \cup P = N

proof or give a counter example that

(x, y, z) \in C^{3}, x^{2} ∣ y z \Rightarrow x ∣ y \lor x ∣ z