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A123322
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Products of 8 distinct primes (squarefree 8-almost primes).
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8
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9699690, 11741730, 13123110, 14804790, 15825810, 16546530, 17160990, 17687670, 18888870, 20030010, 20281170, 20930910, 21111090, 21411390, 21637770, 21951930, 23130030, 23393370, 23993970, 24534510, 25555530, 25571910
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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a(1) = 9699690 = 2*3*5*7*11*13*17*19 = A002110(8).
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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 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
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CROSSREFS
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Cf. A001221, A001222, A005117, A046310, A048692, Squarefree k-almost primes: A000040 (k=1), A006881 (k=2), A007304 (k=3), A046386 (k=4), A046387 (k=5), A067885 (k=6), A123321 (k=7), A115343 (k=9).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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