**Description**

Consider all integer combinations of a^b for 2 <= a <= 5 and 2 <= b <= 5:

2^2=4, 2^3=8, 2^4=16, 2^5=323^2=9, 3^3=27, 3^4=81, 3^5=2434^2=16, 4^3=64, 4^4=256, 4^5=10245^2=25, 5^3=125, 5^4=625, 5^5=3125

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the sequence generated by a^b for 2 <= a <= 100 and 2 <= b <= 100?

**Solution**

let rec powerFx num power endPower arr =

if power > endPower then

arr

else

let newResult = num**power

let newArr = List.append arr [newResult]

powerFx num (power+1.0) endPower newArr

let rec appendPowerFx num endNum power endPower arr =

if num > endNum then

arr

else

let newResult = powerFx num power endPower []

let newArr = List.append arr newResult

appendPowerFx (num+1.0) endNum pow…