triangular number counting function

For a given nonnegative number x, the triangular number counting function counts how many triangular numbersMathworldPlanetmath are not greater than x. The formula is simple:


in sharp contrast to the lack of a formula for the prime counting function π(x). If one accepts 0 as a triangular number, the formula easily accommodates this by the mere addition of 1 after flooring the fraction.


  • 1 Zhi-Wei Sun, “On Sums of Primes and Triangular Numbers” ArXiv preprint, 10 April (2008): 1
Title triangular number counting function
Canonical name TriangularNumberCountingFunction
Date of creation 2013-03-22 18:03:03
Last modified on 2013-03-22 18:03:03
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 5
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A25