%I #6 Feb 12 2013 18:19:26

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,22,24,26,28,30,32,34,36,

%T 38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,84,

%U 90,96,102,108,114,120,126,132,138,144,150,156,162,168,174,180,186,192

%N 3-Round numbers: numbers n such that every number less than n and relatively prime to n has at most three prime factors (counting multiplicities).

%C This sequence, for r=3 prime factors, is finite. Maillet proved that such sequences are finite for any fixed r. The case r=1 is A048597; case r=2 is A122936.

%D Dickson, History of the Theory of Numbers, Vol. I, Chelsea, New York, 1952, p. 134.

%H T. D. Noe, <a href="/A122937/b122937.txt">Table of n, a(n) for n=1..265</a> (complete sequence)

%t Omega[n_] := If[n==1, 0, Plus@@(Transpose[FactorInteger[n]][[2]])]; nn=60060; r=3; moreThanR=Select[Range[nn], Omega[ # ]>r&]; lst={1}; Do[s=Select[Range[n],GCD[n,# ]==1&]; If[Intersection[s,moreThanR]=={}, AppendTo[lst,n]], {n,2,nn}]; lst

%Y Cf. A048597 (very round numbers), A051250, A089016 (largest n-round number).

%K fini,full,nonn

%O 1,2

%A _T. D. Noe_, Sep 21 2006