[seqfan] Re: Sum of omega(k) for k = 1..n

[Ed Jeffery]

Charles Greathouse wrote:

>Regarding A013939, what is the limit of

>(A013939(n) - n log log n)/n?

>Is this constant (roughly a quarter, I think) in the OEIS?

>I wrote

>a(n) = n log log n + O(n).

>but it should really be

?a(n) = n log log n + kn + o(n).

>for some k.

Charles,

Is the first expression the correct one since you should have the relation

a(n) - n*log(log(n)) <= c*O(n), for all n and for some constant c?

Otherwise, since the o(n) term is supposed to dominate, is the term
k*n (in the second expression) redundant? Finally, could

A013939(n) = n*log(log(n)) + O(n/log(n)) (for n large enough)

be a better estimate?

Regards,

Ed Jeffery