Exotic Definitions of Numbers

This section introduces several unique classifications of numbers:

• Happy Number: A number whose sum of the squares of its digits eventually leads to 1. E.g., $19 \rightarrow 1^2+9^2=82 \rightarrow 8^2+2^2=68 \rightarrow \dots \rightarrow 1$.
• Extravagant/Wasteful Number: A number whose prime factorization has more digits than the number itself. E.g., $18 = 2 \times 3^2$. '18' has 2 digits, while '232' has 3.
• Economical/Frugal Number: The opposite of an extravagant number. E.g., $128=2^7$.
• Odious Number: A non-negative number with an odd number of 1s in its binary representation. E.g., $7 = 111_2$.
• Evil Number: A non-negative number with an even number of 1s in its binary representation. E.g., $9 = 1001_2$.