OFFSET
1,1
COMMENTS
Product of 11 not necessarily distinct primes.
Divisible by exactly 11 prime powers (not including 1).
LINKS
D. W. Wilson, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Almost Prime.
FORMULA
Product p_i^e_i with Sum e_i = 11.
a(n) ~ 3628800n log n / (log log n)^10. - Charles R Greathouse IV, May 06 2013
MATHEMATICA
Select[Range[9000], Plus @@ Last /@ FactorInteger[ # ] == 11 &] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2008 *)
Select[Range[30000], PrimeOmega[#]==11&] (* Harvey P. Dale, Jul 13 2013 *)
PROG
(PARI) k=11; start=2^k; finish=30000; v=[]; for(n=start, finish, if(bigomega(n)==k, v=concat(v, n))); v
(PARI) is(n)=bigomega(n)==11 \\ Charles R Greathouse IV, Oct 15 2015
(Python)
from math import isqrt, prod
from sympy import primerange, integer_nthroot, primepi
def A069272(n):
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
def g(x, a, b, c, m): yield from (((d, ) for d in enumerate(primerange(b, isqrt(x//c)+1), a)) if m==2 else (((a2, b2), )+d for a2, b2 in enumerate(primerange(b, integer_nthroot(x//c, m)[0]+1), a) 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, 11)))
return bisection(f, n, n) # Chai Wah Wu, Nov 03 2024
CROSSREFS
Sequences listing r-almost primes, that is, the n such that A001222(n) = r: A000040 (r = 1), A001358 (r = 2), A014612 (r = 3), A014613 (r = 4), A014614 (r = 5), A046306 (r = 6), A046308 (r = 7), A046310 (r = 8), A046312 (r = 9), A046314 (r = 10), this sequence (r = 11), A069273 (r = 12), A069274 (r = 13), A069275 (r = 14), A069276 (r = 15), A069277 (r = 16), A069278 (r = 17), A069279 (r = 18), A069280 (r = 19), A069281 (r = 20). - Jason Kimberley, Oct 02 2011
KEYWORD
nonn,changed
AUTHOR
Rick L. Shepherd, Mar 12 2002
STATUS
approved