1,3

For n odd the value of the arithmetic mean for each possible subset equals (n+1)/2. For n even this value is n/2 or (n+2)/2. If looking after RootMeanSquare for the subset we obtain a sequence[1,0,0,0,0,0,2,...]. We see for example for n=7, A={1,2,3,4,5,6,7} and the only 2 subsets with an integer RootMeanSquare are {1,7}, {1,5,7}. Interestingly the value of RootMeanSquare is 5 for both subsets. So the sequence A140480 RMS numbers is a subsequence of it as a set of divisors of n is clearly a subset of n of the form {1,...,n}.

Arithmetic mean

n=5, A={1,2,3,4,5}. Subsets of A starting with 1 and ending with 5 are : {1,5},{1,2,5},{1,3,5},{1,4,5},{1,2,3,5},{1,2,4,5},{1,3,4,5},{1,2,3,4,5}. Arithmetic mean of the subset is an integer for subsets : {1,5},{1,3,5},{1,2,4,5},{1,2,3,4,5}. Thus a(5)= 4. The value of the ar. mean is 3 for all 4 subsets.

Cf. A140480,

Sequence in context: A129760 A057377 A145811 this_sequence A131772 A021493 A084247

Adjacent sequences: A147977 A147978 A147979 this_sequence A147981 A147982 A147983

nonn

Ctibor O. Zizka (c.zizka(AT)email.cz), Nov 18 2008