OFFSET
1,1
COMMENTS
Numbers of the form p^3*q^3*r^3 where p, q, r are three distinct primes.
The cubic analog of A085986 (squares of 2 distinct primes).
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
FORMULA
EXAMPLE
27000 = 2^3*3^3*5^3. 74088 = 2^3*3^3*7^3. 287496 = 2^3*3^3*11^3.
MATHEMATICA
fQ[n_]:=Last/@FactorInteger[n]=={1, 1, 1}; Select[Range[1000], fQ]^3
PROG
(Python)
from math import isqrt
from sympy import primepi, primerange, integer_nthroot
def A162144(n):
def f(x): return int(n+x-sum(primepi(x//(k*m))-b for a, k in enumerate(primerange(integer_nthroot(x, 3)[0]+1), 1) for b, m in enumerate(primerange(k+1, isqrt(x//k)+1), a+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)**3 # Chai Wah Wu, Aug 30 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Jun 25 2009
EXTENSIONS
Edited by R. J. Mathar, Aug 14 2009
STATUS
approved