[seqfan] sequence, array, some questions

[Kimberling, Clark]

Seqfans,

Let a(n) be the number of positive integers k such that n+k divides n*k.
(Equivalently, 1/n + 1/k = 1/m for some integer m.) The first 30 terms
of a(n) are 0,1,1,2,1,3,1,3,2,4,1,5,1,4,3,4,1,6,1,6,4,4,1,8,2,4,3,6,1,10
.

It is easy to prove that a(n)=1 if and only if n is a prime.  Here's a
corner of the array whose ith row is all n such that a(n)=i, so that row
1 is the primes: 

2....3....5....7....11....13....
4....9....25...49...121...169...
6....8....15...27...35....77...
10...14...16...21...22....26...
12...32...45...243...
18...20...28...63...
44...50...52...68...

Which of the the following statements are true?

(1)  Row i includes all (prime)^i. 

(2)  Every positive integer >1 is in the array.

(3)  The numbers in column 1 are even.

Clark Kimberling