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 A080257 Numbers having at least two distinct or a total of at least three prime factors. 17
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA a(n) = n + O(n/log n). - Charles R Greathouse IV, Sep 14 2015 EXAMPLE 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) MATHEMATICA Select[Range, PrimeNu[#]>1||PrimeOmega[#]>2&] (* Harvey P. Dale, Jul 23 2013 *) PROG (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 CROSSREFS 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 KEYWORD nonn AUTHOR Reinhard Zumkeller, Feb 10 2003 EXTENSIONS Definition clarified by Harvey P. Dale, Jul 23 2013 STATUS approved

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Last modified April 8 17:46 EDT 2020. Contains 333323 sequences. (Running on oeis4.)