A174225 Array: row n consists of the positive integers x for which there are exactly n positive integers y such that x+y divides x*y.

2, 3, 4, 5, 9, 8, 7, 25, 27, 6, 11, 49, 125, 10, 32, 13, 121, 343, 14, 243, 64, 17, 169, 1331, 15, 3125, 729, 12, 19, 289, 2197, 16, 16807, 15625, 18, 256, 23, 361, 4913, 21, 161051, 117649, 20, 6561, 512, 29, 529, 6859, 22

Offset: 1

Author

Clark Kimberling, Mar 12 2010

Keywords

• nonn
• tabl

Comments

Many properties of the array follow easily from Comments at A063647:

1. Every positive integer except 1 occurs, exactly once.

2. Row 1 consists of the primes.

3. Row k includes p^k for all primes p, for k>=1.

4. Row 4 includes all products of two distinct primes.

5. Column 1 consists of even numbers.

Examples

			Corner of the array:
2....3....5....7....11....13....
4....9....25...49...121...169...
8....27...125..343..1331..2197..
6....10...14...15...16....21....
6 is in row 4 because there are 4 numbers y for which
6+y divides 6*y; they are 3,6,12,30.
		

Crossrefs

Cf. A063647.