Corpus ID: 221266453

Recursively abundant and recursively perfect numbers

@article{Fink2020RecursivelyAA,
  title={Recursively abundant and recursively perfect numbers},
  author={Thomas Fink},
  journal={arXiv: Number Theory},
  year={2020}
}
  • 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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References

SHOWING 1-10 OF 14 REFERENCES
Recursively divisible numbers.
  • 1
  • Highly Influential
  • PDF
On the smallest abundant number not divisible by the first k primes
  • 6
On the number of ordered factorizations of natural numbers
  • 15
  • PDF
On Highly Composite Numbers
  • 91
  • PDF
On the maximal order of numbers in the
  • 9
  • PDF
Grandes valeurs et nombres champions de la fonction arithmétique de Kalmár
  • 8
  • PDF
Bounds for the Density of Abundant Integers
  • 32
Odd perfect numbers are greater than 101500
  • 43
  • PDF
Editor
  • 5,621
  • Highly Influential
Recursively divisible numbers, arxiv.org/abs/1912.07979
  • 1912
...
1
2
...