Input a number check if the number is an Unusual Number or generate all Unusual Numbers within a specified range by providing a start and end value.
An Unusual Number is a natural number with a unique factor property: its largest prime factor is greater than its square root. For example: The number 20 is an Unusual Number because its largest prime factor, 5, is greater than \( \sqrt{20} \approx 4.47 \).
All prime numbers are Unusual Numbers because their largest prime factor is the number itself, which is always greater than their square root.
To check if a number is an Unusual Number or generate all Unusual Numbers within a range, follow these steps:
Solution:
1. Prime factorization:
\( 30 = 2 \times 3 \times 5 \), largest prime factor = 5.
2. Calculate the square root:
\(\sqrt{30} \approx 5.48\)
3. Check the prime factor condition:
\(5 \lt 5.48\)
Result: 30 is not an Unusual Number.
Solution:
1. Prime factorization:
\( 102 = 2 \times 3 \times 17 \), largest prime factor = 17.
2. Calculate the square root:
\(\sqrt{102} \approx 10.0995\)
3. Check the prime factor condition:
\(17 \gt 10.0995\)
Result: 102 is an Unusual Number.