With every Mersenne number there is an associated perfect
number, the sum of whose factors exactly equal the number.
I discovered a fascinating thing today, for which I must introduce
some new terminology.
If a number is greater than the sum of its factors, let it be a cold number.
If a number is less than the sum of its factors, let it be a hot number.
Odd numbers are all cold, for instance, and the first hot number is 12.
Nowthen, I found that the ratio of cold numbers to hot numbers is
always about 3. Even when you get up to large numbers [I checked
them all up to about 100,000] the ratio seems to stay right around
3 colds to every hot.
Is there an embarrassingly trivial reason for this? Is there
established terminology for hot and cold numbers? spike
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