OFFSET
1,1
FORMULA
MATHEMATICA
Select[Range[125000], PrimeNu[#]==PrimeOmega[#]==6&] (* Harvey P. Dale, May 14 2014 *)
PROG
(PARI) is(n)=factor(n)[, 2]==[1, 1, 1, 1, 1, 1]~ \\ Charles R Greathouse IV, Sep 14 2015
(PARI) is(n)=omega(n)==6 && bigomega(n)==6 \\ Hugo Pfoertner, Dec 18 2018
(PARI) list(lim)=lim\=1; my(v=List(), L1, L2, L3, L4, P4, P5); forprime(p=13, lim\2310, L1=lim\p; forprime(q=11, min(L1\210, p-2), L2=L1\q; forprime(r=7, min(L2\30, q-2), L3=L2\r; forprime(s=5, min(L3\6, r-2), L4=L3\s; P4=p*q*r*s; forprime(t=3, min(L4\2, s-2), P5=P4*t; forprime(u=2, min(L4\t, t-1), listput(v, P5*u))))))); Set(v) \\ Charles R Greathouse IV, Aug 27 2021
(Python)
from math import prod, isqrt
from sympy import primerange, integer_nthroot, primepi
def A067885(n):
def g(x, a, b, c, m): yield from (((d, ) for d in enumerate(primerange(b+1, isqrt(x//c)+1), a+1)) if m==2 else (((a2, b2), )+d for a2, b2 in enumerate(primerange(b+1, integer_nthroot(x//c, m)[0]+1), a+1) for d in g(x, a2, b2, c*b2, m-1)))
def f(x): return int(n+x-sum(primepi(x//prod(c[1] for c in a))-a[-1][0] for a in g(x, 0, 1, 1, 6)))
kmin, kmax = 0, 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 # Chai Wah Wu, Aug 29 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Mar 02 2002
STATUS
approved