OFFSET
1,4
COMMENTS
A048098(n) is the n-th number k such that all prime divisors of k are <= sqrt(k).
REFERENCES
D. P. Parent, Exercices de théorie des nombres, Les grands classiques, Gauthier-Villars, Edition Jacques Gabay, p. 17.
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = n - (Sum_{p<=sqrt(n)} (p-1)) - Sum_{sqrt(n)<p<=n} floor(n/p). a(n) is the largest k such that A048098(k) <= n. Asymptotically: a(n) = (1-log(2))*n + O(n/log(n)).
From Ridouane Oudra, Nov 07 2019: (Start)
a(n) = n - Sum_{i=1..floor(sqrt(n))} (pi(floor(n/i)) - pi(i)).
a(n) = n - A242493(n). (End)
EXAMPLE
PROG
(PARI) a(n)=n-sum(k=1, floor(sqrt(n)+10^-20), (k-1)*isprime(k))-sum(k=ceil(sqrt(n)+10^-20), n, floor(n/k)*isprime(k))
(PARI) { for (n=1, 1000, a=n - sum(k=1, floor(sqrt(n) + 10^-20), (k-1)*isprime(k)) - sum(k=ceil(sqrt(n) + 10^-20), n, floor(n/k)*isprime(k)); write("b064775.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 24 2009
(Magma) [1] cat [#[k:k in [1..n]|forall{p:p in PrimeDivisors(k)| p le Sqrt(k)}]: n in [2..80]]; // Marius A. Burtea, Nov 08 2019
(Python)
from math import isqrt
from sympy import primepi
def A064775(n): return int(n+sum(primepi(i)-primepi(n//i) for i in range(1, isqrt(n)+1))) # Chai Wah Wu, Oct 05 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, May 11 2002
STATUS
approved