

A080257


Numbers having at least two distinct or a total of at least three prime factors.


18



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

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 primefactor: 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. AdamsWatters, 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 omegasequence (A323023) has sum > 3. Numbers with omegasequence 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[100], PrimeNu[#]>1PrimeOmega[#]>2&] (* Harvey P. Dale, Jul 23 2013 *)


PROG

(Haskell)
a080257 n = a080257_list !! (n1)
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



