kliendanumber

Kliendanumber is a term used in a hypothetical area of number theory. It denotes a natural number n such that the sum of its decimal digits equals the total number of prime factors of n counted with multiplicity (the function Omega(n)). Thus S(n) = Omega(n), where S(n) is the digit-sum and Omega(n) is the big Omega function.

The term is fictional and is used in thought experiments to illustrate how digit-based and factorization-based arithmetic interact. The name is inspired by the imagined mathematician Klienda, and appears in curriculum stories and speculative articles rather than formal research literature.

Examples include 12, 30, and 102: for 12, S(12)=1+2=3 and Omega(12)=3; for 30, S(30)=3 and Omega(30)=3; for 102, S(102)=1+0+2=3 and Omega(102)=3. In typical ranges these numbers are relatively rare, reflecting the differing growth rates of digit sums and Omega.

Notes on properties: There is no simple formula to generate all kliendanumbers. The distribution is irregular, and in the fictional setting researchers discuss whether infinitely many kliendanumbers exist. As n grows, S(n) grows slowly with the number of digits, while Omega(n) grows roughly like log log n, making equality occur at sparse points.

See also: Digit sum; Omega function; additive and multiplicative functions.