Boring numbers

What is the smallest boring number? There’s no such thing, because the title of smallest boring number automatically makes that number interesting.

Herzi Pinki [CC BY-SA 3.0], via Wikimedia Commons
Mathematicians have a lot of names for numbers. Some of my favourites:

  • Lucky numbers (ones that survive the algorithmic sieve of Josephus Flavius, e.g. 163)
  • Polite numbers (add two consecutive integers, and the result is polite, e.g. 34)
  • Betrothed numbers (the sums of their divisors are one apart, e.g. 140 and 195)
  • Untouchable numbers (the sum of any number’s divisors cannot add up to it, e.g. 146)
  • Colossally abundant numbers (numbers with heaps of divisors, e.g. 360)
  • Perfect numbers (a number that is the same as the sum of its divisors, e.g. 28. They’re pretty amazing)
  • Superperfect numbers (forget about perfect numbers, they’re trash. Superperfect numbers are the sum of their divisors and fulfil some other conditions as well. 64 is one.)
  • Hyperperfect numbers (superperfect numbers? I would not be seen in the company of that nonsense. Hyperperfect numbers, e.g. 174, are the only ones for me.)

You get the idea. 64, for example, is interesting because it is a square number, a cube number, a dodecagonal number, a centered triangular number, a perfect square, a perfect cube, an Erdős–Woods number, a self number, a superperfect number…

With so many names for numbers, it’s actually rather difficult to find one that is uninteresting. That doesn’t stop people trying. What’s the first number without a Wikipedia article? In 2014 it was 247. What’s the first number not mentioned in the On-Line Encyclopedia of Integer Sequences (an extremely useful database of numbers and sequences)? In 2014 it was 14228.

Here’s the problem: the fact that it’s the smallest boring number makes it interesting. So it’s no longer boring. But that means it’s no longer the smallest boring number. So now it’s boring again…

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