cp's OEIS Frontend

A217856 Numbers with three prime factors, not necessarily distinct, except cubes of primes.

%I A217856 #19 Jun 24 2014 04:21:05
%S A217856 12,18,20,28,30,42,44,45,50,52,63,66,68,70,75,76,78,92,98,99,102,105,
%T A217856 110,114,116,117,124,130,138,147,148,153,154,164,165,170,171,172,174,
%U A217856 175,182,186,188,190,195,207,212,222,230,231,236,238,242,244,245,246
%N A217856 Numbers with three prime factors, not necessarily distinct, except cubes of primes.
%C A217856 Union of A007304 and A054753.
%C A217856 If n belongs to the sequence, then it can written n=pqr where p, q, r are primes and possibly two, but not all three of them are equal. It is named A3 in the link.
%H A217856 Vincenzo Librandi, <a href="/A217856/b217856.txt">Table of n, a(n) for n = 1..1000</a>
%H A217856 Wushi Goldring, <a href="http://dx.doi.org/10.1016/j.jnt.2005.10.010">Dynamics of the w function and primes</a>, Journal of Number Theory, Volume 119, Issue 1, July 2006, Pages 86-98.
%e A217856 12 = 2^2 * 3 = 2 * 2 * 3, and so it is in the sequence.
%e A217856 27 = 3^3 = 3 * 3 * 3, but that's only one distinct prime and hence 27 is not in the sequence.
%e A217856 30 = 2 * 3 * 5, and so it is in the sequence.
%t A217856 Select[Range[300], PrimeOmega[#] == 3 && PrimeNu[#] > 1 &] (* _Alonso del Arte_, Oct 14 2012 *)
%o A217856 (PARI) atr(n) = {for (i=2, n,if (bigomega(i) == 3 && omega(i) > 1, print1(i, ", ");););}
%o A217856 (PARI) atr(n) = {for (i=2, n,f = factor(i); len = length(f~);if (len > 1,s = sum(i=1, len, f[i,2]);if (s == 3, print1(i,", "))););}
%Y A217856 Cf. A217857.
%K A217856 nonn,easy
%O A217856 1,1
%A A217856 _Michel Marcus_, Oct 13 2012