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A216918 Odd numbers with at least 3 distinct prime factors.

%I A216918 #23 Apr 05 2020 05:03:06
%S A216918 105,165,195,231,255,273,285,315,345,357,385,399,429,435,455,465,483,
%T A216918 495,525,555,561,585,595,609,615,627,645,651,663,665,693,705,715,735,
%U A216918 741,759,765,777,795,805,819,825,855,861,885,897,903,915,935,945,957,969
%N A216918 Odd numbers with at least 3 distinct prime factors.
%C A216918 If "at least" is changed to "exactly" we get A278569. - _N. J. A. Sloane_, Nov 27 2016
%H A216918 Alois P. Heinz, <a href="/A216918/b216918.txt">Table of n, a(n) for n = 1..10000</a>
%H A216918 J. B. Cosgrave, K. Dilcher, <a href="http://www.emis.de/journals/INTEGERS/papers/i39/i39.Abstract.html"> Extensions of the Gauss-Wilson Theorem</a>, Integers: Electronic Journal of Combinatorial Number Theory, 8 (2008), p.11.
%F A216918 Gauss_factorial(floor(a(n)/2), a(n)) == 1 (mod a(n)). (Cf. A216919)
%p A216918 a:= proc(n) option remember; local k;
%p A216918       for k from 2+ `if`(n=1, 103, a(n-1)) by 2
%p A216918         while nops(numtheory[factorset](k))<=2 do od; k
%p A216918     end:
%p A216918 seq (a(n), n=1..100);  # _Alois P. Heinz_, Oct 03 2012
%t A216918 Select[Range[1, 999, 2], (PrimeNu[#] >= 3)&] (* _Jean-François Alcover_, Feb 27 2014 *)
%o A216918 (Sage)
%o A216918 def is_A216918(n):
%o A216918     if n % 2 == 0: return False
%o A216918     return len(n.prime_divisors()) >= 3
%o A216918 def A216918_list(n): return [k for k in srange(1, n + 1, 2) if is_A216918(k)]
%o A216918 A216918_list(969)
%Y A216918 A278569 is a subsequence.
%K A216918 nonn
%O A216918 1,1
%A A216918 _Peter Luschny_, Oct 02 2012