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        riddles >> medium >> How Many Integers
        
(Message started by: navdeep1771 on Apr 12^th, 2019, 9:25am)

Title: How Many Integers
Post by navdeep1771 on Apr 12^th, 2019, 9:25am

How many integers from 1 to 10^6 (both inclusive) are neither perfect squares nor perfect cubes nor perfect fourth powers?

Title: Re: How Many Integers
Post by rmsgrey on Apr 12^th, 2019, 9:59am

Answer: [hide]998910[/hide]

Reasoning:

[hideb]
1000000=1000²=100³=10⁶
1=1²=1³=1⁶

So there are 1000 squares, 100 cubes, and 10 sixth powers (which are both squares and cubes). All fourth powers are also squares, so can be ignored.

So there are 1000+100-10 = 1090 numbers which are squares or cubes (or both) in the range and 1000000-1090 numbers which are neither.
[/hideb]