An ideal friendships

Mathematician Ramanujam didn’t have any close friends and someone asked him the reason. He replied that although he wanted to have close friends but nobody was up to his expectations.

When pressed how he expected his friend to be,  he replied,  "like numbers 220 and 284!"

The person got confused and asked what is the connection between friendship and these numbers!

Ramanujam asked him to find the divisors of each number! 

With much difficulty, the person derived and listed them as, 

220 → 1,2,4,5,10,11,20,22,44,55,110,220

284 →1,2,4,71,142,284

Ramanujam then asked the person to exclude the numbers 220 and 284 and asked the sum of the remaining divisors.

The person was astonished to find,

220 → 1+2+4+5+10+11+20+22+44+55+110=284

284 →1+2+4+71+142=220

Ramanujam explained that an ideal friendship should be like these numbers, to complement each other. Even when one is absent, the other should represent the friend!

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