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A033942
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Positive integers with at least 3 prime factors (counted with multiplicity).
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24
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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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refs;
listen;
history;
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internal format)
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OFFSET
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1,1
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COMMENTS
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A001055(a(n)) > 2; e.g., for a(3)=18 there are 4 factorizations: 1*18 = 2*9 = 2*3*3 = 3*6. - Reinhard Zumkeller, Dec 29 2001
A001222(a(n)) > 2; A054576(a(n)) > 1. - Reinhard Zumkeller, Mar 10 2006
Also numbers such that no permutation of all divisors exists with coprime adjacent elements: A109810(a(n))=0. - Reinhard Zumkeller, May 24 2010
A211110(a(n)) > 3. - Reinhard Zumkeller, Apr 02 2012
A060278(a(n)) > 0. - Reinhard Zumkeller, Apr 05 2013
Volumes of rectangular cuboids with each side > 1. - Peter Woodward, Jun 16 2015
If k is a term then so is k*m for m > 0. - David A. Corneth, Sep 30 2020
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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T. D. Noe, Table of n, a(n) for n = 1..1000
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FORMULA
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Numbers of the form Product p_i^e_i with Sum e_i >= 3.
a(n) ~ n. - Charles R Greathouse IV, May 04 2013
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MAPLE
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with(numtheory): A033942:=n->`if`(bigomega(n)>2, n, NULL): seq(A033942(n), n=1..200); # Wesley Ivan Hurt, Jun 23 2015
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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..]
-- Reinhard Zumkeller, Oct 27 2011
(PARI) is(n)=bigomega(n)>2 \\ Charles R Greathouse IV, May 04 2013
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CROSSREFS
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Cf. A014612.
A101040(a(n))=0.
A033987 is a subsequence; complement of A037143. - Reinhard Zumkeller, May 24 2010
Subsequence of A080257.
See also A002808 for 'Composite numbers' or 'Divisible by at least 2 primes'.
Sequence in context: A152758 A160258 A071280 * A111087 A337373 A166083
Adjacent sequences: A033939 A033940 A033941 * A033943 A033944 A033945
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KEYWORD
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nonn
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AUTHOR
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Jeff Burch
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EXTENSIONS
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Corrected by Patrick De Geest, Jun 15 1998
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STATUS
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approved
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