OFFSET
1,4
COMMENTS
Assuming the Riemann hypothesis, no term exceeds 4. Indeed, let c(n) = (n/phi(n) - (e^gamma)*loglog(n))*sqrt(log(n)). Then, by [Nicolas], the Riemann hypothesis is equivalent to the inequality: for n>=2, c(n)<=c(N), where N is the product of the first 66 primes such that c(N)=4.0628356921... . Since for n in [or "not in", the grammar of the original was ambiguous here - N. J. A. Sloane, Jan 04 2017] A100966, we have c(n)<=0, for those n c(n)<=c(N). Thus assuming the R. H. we see that a(n)<=4.
On the other hand, we conjecture that a(n)<=4 should be true independent of the R. H. If so, then the statement that the R. H. is false would be equivalent to the existence of n for which c(n) is in interval (c(N),5).
LINKS
Peter J. C. Moses, Table of n, a(n) for n = 1..5000
J.-L. Nicolas, Small values of the Euler function and the Riemann hypothesis, Acta Arithmetica, 155(2012), 311-321.
EXAMPLE
The first term in A100966 is k=3. So a(1) = {floor((3/phi(3) - (e^gamma)*loglog(3))*sqrt(log(3)))} = floor((3/2 - 1.78...*0.094...)*1.048...) = 1.
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Dec 09 2016
EXTENSIONS
More terms from Peter J. C. Moses, Dec 09 2016
STATUS
approved