All Questions
4
questions
2
votes
1
answer
125
views
Is there a pattern to the number of unique ways to sum to a number?
I don’t think there is a proper name for these so I will refer to them as “phactors”. Basically, a phactor is a way to sum up to a number using positive real integers that are non zero and not equal ...
- 478
4
votes
1
answer
162
views
Partitions of $2n$ and factorizations of $n$
Let $n$ be any positive integer.
Let $p_1,p_2,...,p_m$ be any positive integers such that no more than one of the $p_i$s is $1$ and $\prod_{i=1}^mp_i=n$.
Finally, let $s_1,s_2,...,s_m$ be any ...
- 2,646
4
votes
1
answer
217
views
Which positive integers can be written in the following form?
I was investigating a generalisation of this problem and found that it reduced to finding where the expression $$\frac{p(p+2m+1)}{2}$$
is an integer, where $p\ge 2$ and $m \ge 0$.
Since exactly one of ...
- 17.3k
6
votes
2
answers
578
views
Is an algebraic formula for the number of cyclic compositions of n known?
From Wikipedia:
In January 2011, it was announced that Ono and Jan Hendrik Bruinier, of the Technische Universität Darmstadt, had developed a finite, algebraic formula determining the value of p(n) (...
- 1,129