LENGTH SPECTRA OF NATURAL NUMBERS
Wai Yan Pong · International Journal of Number Theory · 2009
A natural number n can generally be written as a sum of m consecutive natural numbers for various values of m ≥ 1. The length spectrum of n is the set of these admissible m. Two numbers are spectral equivalent if they have the same length spectrum. We show how to compute the equivalence classes of this relation. Moreover, we show that these classes can only have either 1,2 or infinitely many elements.