sum{k=1 to m} 1/k^n

[Leroy Quet]

Consider the sequence where each term is a numerator of at least one 
reduced rational
sum{k=1 to m} 1/k^n,
taken over all positive integers m and n.

So, unless I carelessly erred, the sequence begins:

1, 3, 5, 9, 11, 17, 25, 33, 49,...


(Not in EIS.)

3 things:

1) Except for 1 and 49, do any of the terms of this sequence correspond
with more than one {m,n}?

(49 is numerator when m = 6 and n = 1, and when m = 3 and n =2.)

2) We can consider also the sequence of denominators too, obviously.

3) Generally, we can apply the idea here to generating other sequences:
If we have any 2(or more)-index sequence {a(m,n)}, where the terms 
consist of only a subset of all integers, then we can form the sequence 
which contains the distinct integers (in numerical order) of {a(m,n)}.

thanks,
Leroy Quet