A perfect number is defined as a positive integer which is the sum of its proper positive divisors, that is, the sum of the positive divisors excluding the number itself.
Take 6. divisors are 1, 2, 3, and 6. (1+2+3+6)/2=6 or 1+2+3=6. Here are a few known perfect numbers.
6,
28,
496,
8128,
33550336,
8589869056,
137438691328,
2305843008139952128,
2658455991569831744654692615953842176,
19156194260823610729479337808430363813099732154816 9216,
13164036458569648337239753460458722910223472318386 943117783728128,
14474011154664524427946373126085988481573677491474 835889066354349131199152128,
23562723457267347065789548996709904988477547858392 60071014302759750633728317862223973036553960260056 13602555664625032701750528925780432155433824984287 77152427010394496918664028644534128033831439790236 83862403317143592235664321970310172071316352748729 87474006478019395871659364010874193756490579185494 92160555646976,
And so on. The largest known perfect number is 19616714 digits long. You can view it here -
http://amicable.adsl.dk/aliquot/c1/perfx44.txt
you can find a list of them all here -
http://amicable.homepage.dk/perfect.htm