multiperfect number completeness
Don Reble
djr at nk.ca
Tue Nov 4 02:45:10 CET 2003
> From the special form of the even perfects, it should be easy to
> say yea-or-nea to the whole group. From your evidence below, it
> looks like N>6 -> Nay.
Ah, of course. The perfect number 2^(p-1)*(2^p-1) is eliminated by the
sum of the p'th powers of the factors. 6 is the "odd" man in, because
it's Mersenne exponent is an _even_ prime. Thanks, Rich.
> Given that there are thousands of MPFNs > 6e78, and you've checked the lot-2,
> it looks like your sequence may have come to an end. Does simply checking
> divisor-sum and sum-of-cubes give a thicker sequence?
Yes. Checking the same "lot-2", I find 223 numbers in the thicker
sequence. And all those perfect numbers are in, except 4*(2^3-1), so
the last two make the total 225.
--
Don Reble djr at nk.ca
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