A quite computationally challenging integer sequence I know is the sequence of odd positive integers $n$ for which $\sigma(n)-2n=6$. Here $\sigma(n)$ denotes the sum of positive divisors of $n$. Only 8 terms of this sequence are known, and the largest one, 815634435, was computed on 2011 (sequence A141548). Larger terms of this sequence could be related to an eventual proof of the existence of odd weird numbers, an old open question raised by Erdös and Benkoski.

A quite computationally challenging integer sequence I know is the sequence of odd positive integers $n$ for which $2n-\sigma(n)=6$, i.e. $n$ with ''abundance'' -6. Here $\sigma(n)$ denotes the sum of positive divisors of $n$. Only 8 terms of this sequence are known, and the largest one, 815634435, was computed on 2011 (sequence A141548). Larger terms of this sequence could be related to an eventual proof of the existence of odd weird numbers, an old open question raised by Erdös and Benkoski.