For introduction, Ethiointegers are integers which get reversed when multiplied by another number.

For instance,

2178 * 4 = 8712

1089 * 9 = 9801

I couldn't find such numbers, even by another name anywhere else except in one journal which I think is not electronically accessible.

**My question**: Has numbers like this been treated anywhere? If so, what interesting properties do they have?

[E.g. One property I consider interesting: sumofdivisors(1089) = 1729 = 1728 + 1 (Hardy's taxi number 12^3 + 1^3, more about this sum ), also 1728 is a rearrangement of 2178!]

[Added later] Eulertotient(2178) = Eulertotient(1089)

a priorireason this has to be the case. It's quite possible that something mathematically interesting could emerge. At any rate, it's entirely reasonable to ask if anything is known about such numbers. – Timothy Chow Jun 13 '10 at 1:29