Numbers can be many things to many people. They can be Happy, Unhappy, Evil, or Odious. Perhaps now’s time to turn to Weird numbers (like 70)
“A weird number is a number n for which σ(n)>2n and such that n is not a sum of distinct proper divisors of n.”
Here is Dr. Giuseppe Melfi, professor at the University of the Applied Sciences Western Switzerland and lecturer at the University of Neuchâtel, explaining his paper ‘On the conditional infiniteness of primitive weird numbers’ which is published in the Journal of Number Theory, Volume 147, February 2015, Pages 508–514.
BONUS: May we robustly recommend the website(s) of Dr. Tanya Khovanova, who is a freelance mathematician and a Research Affiliate at the Mathematics Department of MIT.
Dr. Khovanova not only maintains a real-time online a number profiling service (just enter a number to discover its personality) but also provides a growing list of Number Gossip Properties – which inspired this short Improbable series.