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A080257
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Numbers having at least two distinct or a total of at least three prime factors.
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17
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6, 8, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100
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OFFSET
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1,1
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COMMENTS
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Complement of A000430; A080256(a(n)) > 3.
A084114(a(n)) > 0, see also A084110.
Also numbers greater than the square of their smallest prime-factor: a(n)>A020639(a(n))^2=A088377(a(n));
a(n)>A000430(k) for n<=13, a(n) < A000430(k) for n>13.
Numbers with at least 4 divisors. - Franklin T. Adams-Watters, Jul 28 2006
Union of A024619 and A033942; A211110(a(n)) > 2. - Reinhard Zumkeller, Apr 02 2012
Also numbers > 1 that are neither prime nor a square of a prime. Also numbers whose omega-sequence (A323023) has sum > 3. Numbers with omega-sequence summing to m are: A000040 (m = 1), A001248 (m = 3), A030078 (m = 4), A068993 (m = 5), A050997 (m = 6), A325264 (m = 7). - Gus Wiseman, Jul 03 2019
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = n + O(n/log n). - Charles R Greathouse IV, Sep 14 2015
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EXAMPLE
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8=2*2*2 and 10=2*5 are terms; 4=2*2 is not a term.
From Gus Wiseman, Jul 03 2019: (Start)
The sequence of terms together with their prime indices begins:
6: {1,2}
8: {1,1,1}
10: {1,3}
12: {1,1,2}
14: {1,4}
15: {2,3}
16: {1,1,1,1}
18: {1,2,2}
20: {1,1,3}
21: {2,4}
22: {1,5}
24: {1,1,1,2}
26: {1,6}
27: {2,2,2}
28: {1,1,4}
30: {1,2,3}
32: {1,1,1,1,1}
(End)
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MATHEMATICA
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Select[Range[100], PrimeNu[#]>1||PrimeOmega[#]>2&] (* Harvey P. Dale, Jul 23 2013 *)
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PROG
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(Haskell)
a080257 n = a080257_list !! (n-1)
a080257_list = m a024619_list a033942_list where
m xs'@(x:xs) ys'@(y:ys) | x < y = x : m xs ys'
| x == y = x : m xs ys
| x > y = y : m xs' ys
-- Reinhard Zumkeller, Apr 02 2012
(PARI) is(n)=omega(n)>1 || isprimepower(n)>2
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CROSSREFS
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Cf. A001248, A001221, A001222, A006881, A030078, A088381, A088383, A000005.
Cf. A060687, A118914, A323014, A323023, A325249.
Sequence in context: A071278 A079772 A080731 * A331201 A050199 A268388
Adjacent sequences: A080254 A080255 A080256 * A080258 A080259 A080260
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Feb 10 2003
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EXTENSIONS
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Definition clarified by Harvey P. Dale, Jul 23 2013
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STATUS
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approved
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