Jonathan. Frech’s WebBlog

A325902 (#220)

Jonathan Frech,

Fifty is a peculiar in­te­ger.
When looking at its neighbors — the largest in­te­ger strictly beneath and the smallest strictly above —, more specifically their prime factorization, one finds

$$49=\underbrace{7^2<50<3\cdot 17}_{7+7+3=17}=51.$$$$49=\underbrace{7^2<50<3\cdot 17}_{7+7+3=17}=51.$$$$49=\underbrace{7^2<50<3\cdot 17}_{7+7+3=17}=51.$$

Notably, there exists a partition of the neighbor’s factors into two multisets such that both parts’ sums equal another.

Positive integers with the above described prop­er­ty can be found in my most recent addition to the OEIS: sequence A325902.