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A033987
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Numbers that are divisible by at least 4 primes (counted with multiplicity).
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17
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16, 24, 32, 36, 40, 48, 54, 56, 60, 64, 72, 80, 81, 84, 88, 90, 96, 100, 104, 108, 112, 120, 126, 128, 132, 135, 136, 140, 144, 150, 152, 156, 160, 162, 168, 176, 180, 184, 189, 192, 196, 198, 200, 204, 208, 210, 216, 220, 224, 225, 228, 232, 234, 240, 243
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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 proper divisors exists with coprime adjacent elements: A178254(a(n)) = 0. - Reinhard Zumkeller, May 24 2010
Also, numbers that can be written as a product of at least two composites, i.e., admit a nontrivial factorization into composites. - Felix Fröhlich, Dec 22 2018
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LINKS
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FORMULA
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Product p_i^e_i with Sum e_i >= 4.
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MAPLE
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MATHEMATICA
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Select[Range[300], PrimeOmega[#]>3&] (* Harvey P. Dale, Mar 20 2016 *)
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PROG
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(Python)
from math import prod, isqrt
from sympy import primerange, integer_nthroot, primepi
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+primepi(x)+sum(sum(primepi(x//prod(c[1] for c in a))-a[-1][0] for a in g(x, 0, 1, 1, i)) for i in range(2, 4)))
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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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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