I've been exploring nice numbers. By "nice numbers" I of course refer to numbers that aren't mean. :-) I started by searching for sets of integers that don't contain the arithmetic mean of any pair of their elements. I learned that this is well explored territory. A greedy algorithm found a sequence which, when I looked it up in OEIS, was described as the numbers expressible in ternary without the digit 2. A005836. It's not obvious to me why that should be. Comments confirmed that the property I noticed is well known, but phrased in such a way that my search didn't find it. Next I modified my program to search for sets of integers that don't contain the *geometric* mean of any of their elements. It generated what turned out to be A000452, numbers whose prime factorization only contains exponents expressible in ternary without the digit 2. Again, comments confirmed that the property I noticed is well known, but, again, phrased in such a way that my search didn't find it. I'm seeking a set of totally nice numbers, a set of integers which doesn't contain any power mean of any pairs of elements. (I consider the geometric mean to be the zeroth power mean, which it technically is only in the limit.) Has anyone done this already? Thanks.