I define an increasing function from triangular numbers to triangular numbers and prove it preserves [mathematical symbol]. I conjecture that whether a triangular number is in the image of this function is related to the magnitude of [mathematical symbol] on the triangular number. Parallel theorems and conjectures exist for pentagonal numbers. I also make conjectures about the partial sums of [mathematical symbol] on the triangular numbers along with a conjecture about the sums of absolute values of [mathematical symbol] on the squares.
More Triangular Number Results.
Journal of the Minnesota Academy of Science, Vol. 62 No.1, 1-2.
Retrieved from https://digitalcommons.morris.umn.edu/jmas/vol62/iss1/2