Can a Prime Power be a Member of an Amicable Pair?
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Open Question
It is not known whether it is possible for a prime power to be a member of an amicable pair.
Progress
If $p^n$ is a member of an amicable pair, then:
- $p^n > 10^{1500}$
- $n > 1400$
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $220$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $220$