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A033942
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Positive integers with at least 3 prime factors (counted with multiplicity).
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36
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8, 12, 16, 18, 20, 24, 27, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 63, 64, 66, 68, 70, 72, 75, 76, 78, 80, 81, 84, 88, 90, 92, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 116, 117, 120, 124, 125, 126, 128, 130, 132, 135, 136, 138, 140, 144
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OFFSET
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1,1
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COMMENTS
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Also numbers such that no permutation of all divisors exists with coprime adjacent elements: A109810(a(n))=0. - Reinhard Zumkeller, May 24 2010
Volumes of rectangular cuboids with each side > 1. - Peter Woodward, Jun 16 2015
Numbers k with a pair of proper divisors of k, (d1,d2), such that d1 < d2 and gcd(d1,d2) > 1. - Wesley Ivan Hurt, Jan 01 2021
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LINKS
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FORMULA
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Numbers of the form Product p_i^e_i with Sum e_i >= 3.
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MAPLE
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MATHEMATICA
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Select[ Range[150], Plus @@ Last /@ FactorInteger[ # ] > 2 &] (* Robert G. Wilson v, Oct 12 2005 *)
Select[Range[150], PrimeOmega[#]>2&] (* Harvey P. Dale, Jun 22 2011 *)
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PROG
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(Haskell)
a033942 n = a033942_list !! (n-1)
a033942_list = filter ((> 2) . a001222) [1..]
(Python)
from sympy import factorint
def ok(n): return sum(factorint(n).values()) > 2
(Python)
from math import isqrt
from sympy import primepi, primerange
def f(x): return int(n+primepi(x)+sum(primepi(x//k)-a for a, k in enumerate(primerange(isqrt(x)+1))))
kmin, kmax = 1, 2
while f(kmax) >= kmax:
kmax <<= 1
while True:
kmid = kmax+kmin>>1
if f(kmid) < kmid:
kmax = kmid
else:
kmin = kmid
if kmax-kmin <= 1:
break
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CROSSREFS
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See also A002808 for 'Composite numbers' or 'Divisible by at least 2 primes'.
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KEYWORD
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nonn,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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