Dear Spike,
In keeping with the Three bears, the perfect numbers would be "just
right." The proper terminology to apply to these numbers are abundant (M4825,
A5010) and deficient (M0514, A5100) numbers. Odd primitive abundant numbers
(M5486, A6038) are:
945, 1575, 2205, 3465, 4095, 5355, 5775, 5985, 6435, 6825, 7245, 7425, 8085,
8415, 8925, 9135, 9555, 9765, 11655, 12705, 12915, 13545, 14805, 15015, 16695,
18585, ..., .
Mathimatically yours,
Robert G. Wilson v,
PhD ATP / CF&GI
Spike Jones wrote:
> 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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