Two hundred eighty-four is the second half of history's first documented amicable pair, paired with 220 in a relationship known to mathematicians since antiquity — and while its companion number, 220, typically gets top billing in popular accounts of the pair, 284's own side of the relationship is every bit as essential to what makes the pairing work.
The defining property: the proper divisors of 284 (1, 2, 4, 71, and 142 — notably a much shorter list than 220's eleven proper divisors, since 284's factorization, 2²×71, is considerably simpler) sum to exactly 220 (1+2+4+71+142=220). And, completing the reciprocal relationship, the proper divisors of 220 sum right back to 284. Neither number is self-sufficient the way a perfect number is; each one's identity within this relationship depends entirely on the other, which is precisely the property that gives amicable numbers their name and their long-standing symbolic association with mutual friendship, dating back to Pythagorean tradition in ancient Greece.
It's worth noting the structural asymmetry between the pair's two halves, since it's genuinely interesting and often overlooked in popular retellings: 284's factorization (2² × 71) is far simpler than 220's (2² × 5 × 11), giving 284 only six total divisors compared to 220's twelve. Despite this considerable structural difference — one number built from just two distinct primes, the other from three — their proper-divisor sums still land on each other exactly. This is part of why amicable pairs are considered a genuinely delicate, non-obvious mathematical phenomenon rather than an easily-anticipated pattern: there's no simple, general reason to expect two structurally different numbers to relate this precisely, which is exactly why finding new amicable pairs (beyond the general formulas mathematicians like Thābit ibn Qurra and Euler eventually developed) has remained a genuinely difficult problem across the history of number theory.
284's specific role in later cultural and numerological readings of the pair tends to be treated as secondary to 220's in most historical accounts, largely because early source material more often introduces the pair by leading with 220 — but the mathematical relationship is, by definition, entirely symmetric between the two, and 284 deserves recognition as an equal, essential half of the structure rather than merely 220's counterpart. Both numbers only earn their place in this list of notable values because of the relationship between them; taken in total isolation, without reference to its partner, 284 has no distinguishing arithmetic property beyond being an ordinary composite number.
The amicable-pair relationship between 220 and 284 remains the clearest, most historically documented starting point for understanding this entire branch of recreational number theory — every later amicable pair discovered, from Thābit ibn Qurra's algebraic formula through Euler's extensive 18th-century search to the many thousands identified by modern computer search, is understood and explained today as an extension of the exact same reciprocal divisor-sum relationship first documented in this original, smallest pair.
284's comparatively simple factorization (2² × 71) also makes it a useful entry point for anyone verifying the pair's arithmetic by hand for the first time — its six total divisors are quick to list, and confirming that they sum to 220 takes only a moment, a nice contrast with 220's own eleven-divisor list, which takes a bit more patience to work through completely but arrives at the identical, mutually confirming result.
284 rarely appears in popular retellings without its partner, and that's arguably the most honest way to present it — unlike most numbers on this list, which carry a distinguishing property in isolation, 284's entire claim to notability is defined relationally, through its specific pairing with 220, rather than through any standalone feature of the number itself.
Later mathematicians extending the search for amicable pairs beyond 220 and 284 often specifically tested numbers with a similarly simple factorization structure to 284's, since a shorter divisor list is considerably faster to sum and check by hand or by early computational methods than the more sprawling divisor lists of highly composite numbers — a small but genuine piece of practical strategy underlying how this branch of number theory's early search efforts were actually conducted, long before modern computing made exhaustive search across enormous ranges feasible. That practical constraint shaped which pairs got discovered first, not just which pairs happen to exist.