

A033987


Numbers that are divisible by at least 4 primes (counted with multiplicity).


15



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

1,1


COMMENTS

Complement of A037144: A001222(a(n)) > 3; A117358(a(n)) > 1.  Reinhard Zumkeller, Mar 10 2006
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 FrÃ¶hlich, Dec 22 2018


LINKS

T. D. Noe, Table of n, a(n) for n=1..1000


FORMULA

Product p_i^e_i with Sum e_i >= 4.
A001055(a(n)) > A033273(a(n)).  JuriStepan Gerasimov, Nov 09 2009


MAPLE

with(numtheory): A033987:=n>`if`(bigomega(n)>3, n, NULL): seq(A033987(n), n=1..300); # Wesley Ivan Hurt, May 26 2015


MATHEMATICA

Select[Range[300], PrimeOmega[#]>3&] (* Harvey P. Dale, Mar 20 2016 *)


PROG

(PARI) is(n)=bigomega(n)>3 \\ Charles R Greathouse IV, May 26 2015


CROSSREFS

Subsequence of A033942; A178212 is a subsequence.
Cf. A014613, A001055, A033273.
Sequence in context: A114415 A320141 A225903 * A140349 A088493 A074451
Adjacent sequences: A033984 A033985 A033986 * A033988 A033989 A033990


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Patrick De Geest, Jun 15 1998


STATUS

approved



