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Hometriangular number counting function

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# triangular number counting function

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

$\lfloor\frac{-1+\sqrt{8x+1}}{2}\rfloor,$ |

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

# References

- 1 Zhi-Wei Sun, “On Sums of Primes and Triangular Numbers” ArXiv preprint, 10 April (2008): 1

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## Mathematics Subject Classification

11A25*no label found*

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