220

Mains supply across most of Europe, Asia and Africa was nominally 220 volts while the United Kingdom and Ireland used 240. The two were harmonised on paper in the 1990s to a nominal 230 volts with a tolerance band wide enough to cover both, so most supplies did not physically change and 'a 220-volt country' remains ordinary speech for anywhere outside the 100–127 volt group. The practical point for a traveller is the frequency and the plug rather than the voltage: modern chargers accept the whole range.

220 yards is one furlong, an eighth of a mile, and was the standard sprint distance in imperial athletics until metrication replaced it with 200 metres — a distance about 1.3 metres shorter, which is why pre-1970s records are not directly comparable with modern ones. The furlong survives in horse racing, where race distances in Britain, Ireland and the United States are still quoted in miles and furlongs.

220's proper divisors are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, and they sum to 284. The reason the pair is scarce is that the divisor-sum function is erratic: 220 has twelve divisors and 284 has only six, so the two arrive at each other's totals by very different routes. Around a billion amicable pairs are now known, and every one has been found by search rather than by a formula that generates them.

220 is the tenth tetrahedral number: stack ten triangular layers of oranges, 1 then 3 then 6 and so on, and the pile contains 220. The formula n(n+1)(n+2)/6 gives 10 × 11 × 12 ÷ 6 = 220. It is the same counting that gives the number of ways to choose three items from twelve, which is why tetrahedral numbers appear in the third diagonal of Pascal's triangle.

The proper divisors of 220 sum to 284 and those of 284 sum back to 220. The Pythagoreans knew the pair, and it appears in medieval talismans as a symbol of friendship — a documented historical use, which is a different claim from the property meaning anything.