OFFSET
1,1
COMMENTS
It is conjectured that x is always bounded.
If p and q are primes < sqrt(x) that do not divide x, then p*q is in RRS(x). Thus the number of composites in RRS(x) is at least (pi(sqrt(x)) - log_2(x))^2/2. If x is too large, this must be greater than n. Thus suppose N is large enough that pi(sqrt(N)) > 2*sqrt(2*n) and for all x >= N, pi(sqrt(x)) > 2*log_2(x). Then a(n) <= N. It appears that the condition pi(sqrt(x)) > 2*log_2(x) is true for all x >= 103^2. - Robert Israel, Aug 26 2018, corrected Feb 24 2020
From Giovanni Resta, Feb 25 2020: (Begin)
The following bounds (valid for n>1) are known:
primepi(n) < 1.256*n/log(n),
omega(n) > 0,
phi(n) > n/(3/log(log(n)) + exp(g)*log(log(n))), where g = A001620 = 0.5770836... is the Euler-Mascheroni constant.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000
EXAMPLE
PROG
(PARI) lista(nn) = {my(v = vector(10^5, n, eulerphi(n) - (primepi(n) - omega(n)))); vector(nn, k, if (#(w=Vec(select(x->(x==k), v, 1))) == 0, 0, vecmax(w))); } \\ Michel Marcus, Feb 23 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Oct 10 2002
STATUS
approved