An extravagant number (also known as a wasteful number) is a natural number that has fewer digits than the number of digits in its prime factorization (including exponents).[1] For example, in base-10 arithmetic 4 = 2², 6 = 2×3, 8 = 2³, and 9 = 3² are extravagant numbers.
Extravagant numbers can be defined in any base. There are infinitely many extravagant numbers, no matter what base is used.[1]
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