

A279291


a(n) = floor((k/phi(k)  (e^gamma)*loglog(k))*sqrt(log(k))) where k = A100966(n).


1



1, 1, 0, 2, 1, 0, 1, 2, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 1, 0, 2, 1, 0, 1, 2, 1, 0, 0, 1, 1, 2, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 2, 0, 2, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1
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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), 311321.


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

Cf. A000010, A001620, A279161, A100966.
Sequence in context: A129634 A266825 A066438 * A051126 A168120 A063933
Adjacent sequences: A279288 A279289 A279290 * A279292 A279293 A279294


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Dec 09 2016


EXTENSIONS

More terms from Peter J. C. Moses, Dec 09 2016


STATUS

approved



