Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
22=4, 23=8, 24=16, 25=32 32=9, 33=27, 34=81, 35=243 42=16, 43=64, 44=256, 45=1024 52=25, 53=125, 54=625, 55=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 ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?
In [1]:
require 'set'
Out[1]:
In [7]:
def distinct_powers(a, b)
result = Set.new
(2..a).each do |x|
(2..b).each do |y|
result.add x**y
end
end
return result
end
distinct_powers(5, 5)
Out[7]:
In [10]:
distinct_powers(100, 100).count
Out[10]:
In [ ]: