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A123321
Products of 7 distinct primes (squarefree 7-almost primes).
14
510510, 570570, 690690, 746130, 870870, 881790, 903210, 930930, 1009470, 1067430, 1111110, 1138830, 1193010, 1217370, 1231230, 1272810, 1291290, 1345890, 1360590, 1385670, 1411410, 1438710, 1452990, 1504230, 1540770
OFFSET
1,1
COMMENTS
Intersection of A005117 and A046308.
Intersection of A005117 and A176655. - R. J. Mathar, Dec 05 2016
LINKS
EXAMPLE
a(1) = 510510 = 2*3*5*7*11*13*17 = A002110(7).
MATHEMATICA
f7Q[n_]:=Last/@FactorInteger[n]=={1, 1, 1, 1, 1, 1, 1}; lst={}; Do[If[f7Q[n], AppendTo[lst, n]], {n, 9!}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 26 2008 *)
Select[Range[1600000], PrimeNu[#]==7&&SquareFreeQ[#]&] (* Harvey P. Dale, Sep 19 2013 *)
PROG
(PARI) is(n)=omega(n)==7 && bigomega(n)==7 \\ Hugo Pfoertner, Dec 18 2018
(Python)
from math import isqrt, prod
from sympy import primerange, integer_nthroot, primepi
def A123321(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, 7)))
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
Cf. A005117, A046308, A048692, Squarefree k-almost primes: A000040 (k=1), A006881 (k=2), A007304 (k=3), A046386 (k=4), A046387 (k=5), A067885 (k=6), A123322 (k=8), A115343 (k=9).
Sequence in context: A250057 A230619 A176655 * A258362 A147574 A046325
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Sep 25 2006
EXTENSIONS
More terms from Vladimir Joseph Stephan Orlovsky, Aug 26 2008
STATUS
approved