OFFSET
1,1
COMMENTS
This set (S say) has density d(S) = Log(2) - Benoit Cloitre, Jun 12 2002
Finch defines a positive integer N to be "jagged" if its largest prime factor is > sqrt(N). - Frank Ellermann, Apr 21 2011
REFERENCES
S. R. Finch, Mathematical Constants, 2003, chapter 2.21.
LINKS
Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)
Eric Weisstein's World of Mathematics, Greatest Prime Factor
EXAMPLE
9=3*3 is not "jagged", but 10=5*2 is "jagged": 5 > sqrt(10).
20=5*2*2 is "jagged", but not squarefree, cf. A005117.
MATHEMATICA
Reap[For[n = 2, n <= 102, n++, f = FactorInteger[n][[-1, 1]]; If[f > Sqrt[n], Sow[n]]]][[2, 1]] (* Jean-François Alcover, May 16 2014 *)
PROG
(PARI) { n=0; for (m=2, 10^9, f=factor(m)~; if (f[1, length(f)]^2 > m, write("b064052.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 06 2009
(Python)
from math import isqrt
from sympy import primepi
def A064052(n):
def f(x): return int(n+x-sum(primepi(x//i)-primepi(i) for i in range(1, isqrt(x)+1)))
def bisection(f, kmin=0, kmax=1):
while f(kmax) > kmax: kmax <<= 1
while kmax-kmin > 1:
kmid = kmax+kmin>>1
if f(kmid) <= kmid:
kmax = kmid
else:
kmin = kmid
return kmax
return bisection(f) # Chai Wah Wu, Sep 01 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Dean Hickerson, Aug 28 2001
STATUS
approved