Ruth and Aaron

Two consecutive integers a and b are considered a Ruth-Aaron pair if the sum of the prime factors of a is equal to the sum of the prime factors of b.

Two definitions exist:

1. Summing up distinct prime factors. For example, 24 and 25 constitute a Ruth-Aaron pair by this definition. 8 and 9 do not.

P24 = [2, 3]  # sum = 5

P25 = [5]  # sum = 5, equal to 24

P8 = [2]  # sum = 2

P9 = [3]  # sum = 3

1. Summing up repeated prime factors. By this definition, 24 and 25 do not constitute a Ruth-Aaron pair. But 8 and 9 do.

P24 = [2, 2, 2, 3]  # sum = 9

P25 = [5, 5]  # sum = 10

P8 = [2, 2, 2]  # sum = 6

P9 = [3, 3]  # sum = 6, equal to 8

If two consecutive numbers have only distinct prime factors and have equal sums of prime factors, they are considered Ruth-Aaron pairs by both definitions.

P77 = [7, 11]  # sum = 18

P78 = [2, 3, 13]  # sum = 18

Create a function that takes a number n and returns:

1. False if it is not part of a Ruth-Aaron pair.
2. A 2-element list if it is part of a Ruth-Aaron pair.
   • The first element should be "Ruth" if n is the smaller number in the pair, or "Aaron" if it is the larger.
   • The second element should be 1 if n is part of a Ruth-Aaron pair under the first definition (sum of distinct prime factors), 2 if it qualifies by the second definition, 3 if it qualifies under both.

Examples

ruth_aaron(5) ➞ ["Ruth", 3]

ruth_aaron(25) ➞ ["Aaron", 1]

ruth_aaron(9) ➞ ["Aaron", 2]

ruth_aaron(11) ➞ False

Notes

N/A