Corpus ID: 221266453

Recursively abundant and recursively perfect numbers

  title={Recursively abundant and recursively perfect numbers},
  author={Thomas Fink},
  journal={arXiv: Number Theory},
  • Thomas Fink
  • Published 2020
  • Mathematics
  • arXiv: Number Theory
The divisor function $\sigma(n)$ sums the divisors of $n$. We call $n$ abundant when $\sigma(n) - n > n$ and perfect when $\sigma(n) - n = n$. I recently introduced the recursive divisor function $a(n)$, the recursive analog of the divisor function. It measures the extent to which a number is highly divisible into parts, such that the parts are highly divisible into subparts, so on. Just as the divisor function motivates the abundant and perfect numbers, the recursive divisor function motivates… Expand

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