Sequences of density zeta(k) - 1

TL;DR

This paper offers a novel interpretation of the sequence (k) - 1, derived from the Riemann zeta function, as probabilities within a specific number theoretic framework, inspired by a challenge at a mathematicians' gathering.

Contribution

It introduces a new probabilistic interpretation of the sequence (k) - 1, connecting the Riemann zeta function to number theory in a novel way.

Findings

The sequence (k) - 1 sums to 1.

Provides a probabilistic model for the sequence.

Connects the Riemann zeta function to number theoretic probabilities.

Abstract

At a social gathering of mathematicians, Herb Wilf noted that the numbers $\zeta(k) - 1$ sum to 1, and challenged the assembly to interpret the sequence as probabilities in some interesting number theoretic context. This short note provides one such interpretation.