OFFSET
1,1
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..29422 (first 10000 terms from Rick Shepherd)
EXAMPLE
a(1) = 9699690 = 2*3*5*7*11*13*17*19 = A002110(8).
MAPLE
N:= 3*10^7: # to get all terms <= N
pmax:= floor(N/mul(ithprime(i), i=1..7)):
Primes:= select(isprime, [2, seq(i, i=3..pmax, 2)]):
sort(select(`<`, map(convert, combinat:-choose(Primes, 8), `*`), N)); # Robert Israel, Dec 18 2018
MATHEMATICA
f8Q[n_]:=Last/@FactorInteger[n]=={1, 1, 1, 1, 1, 1, 1, 1}; lst={}; Do[If[f8Q[n], AppendTo[lst, n]], {n, 10!, 11!}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 26 2008 *)
Take[ Sort[ Times @@@ Subsets[ Prime@ Range@ 15, {8}]], 22] (* Robert G. Wilson v, Dec 18 2018 *)
PROG
(PARI) is(n)=issquarefree(n)&&omega(n)==8 \\ Charles R Greathouse IV, Feb 01 2017, corrected (following an observation from Zak Seidov) by M. F. Hasler, Dec 19 2018
(PARI) is(n) = my(f = factor(n)); omega(f) == 8 && bigomega(f) == 8 \\ David A. Corneth, Dec 18 2018
(Python)
from math import isqrt, prod
from sympy import primerange, integer_nthroot, primepi
def A123322(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, 8)))
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, Aug 31 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Sep 25 2006
EXTENSIONS
Edited by Robert Israel, Dec 18 2018
STATUS
approved