Wednesday, 7 May 2025

Maths: Amicable numbers

Charles Babbage’s Difference Engine, a forerunner of the modern computer. Lots of people have heard of Charles, but his son Herschel Babbage, a meticulous Australian explorer is hardly known.
Everything is connected!

The number 220 is the smaller number in the first pair of amicable numbers. The other number in the pair is 284. The proper divisors of 220 (1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110) sum to 284, while the proper divisors of 284 (1, 2, 4, 71 and 142) sum to 220. Up until 1946, there were 390 known pairs of amicable numbers, but by 2007, there were almost 12 million known pairs. The number reached 1,229,544,099, according the Amicable pairs list (https://sech.me/ap/ (last seen May 2025), which is available on the internet. It will be higher, by the time you read this…science is like that, and so is mathematics. 

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