Search: id:A122937
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%I A122937
%S A122937 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 A122937 38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,84,
%U A122937 90,96,102,108,114,120,126,132,138,144,150,156,162,168,174,180,186,192
%N A122937 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 A122937 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 A122937 Dickson, History of the Theory of Numbers, Vol. I, Chelsea, New York, 
               1952, p. 134.
%H A122937 T. D. Noe, <a href="b122937.txt">Table of n, a(n) for n=1..265</a> [complete 
               list]
%t A122937 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 A122937 Cf. A048597 (very round numbers), A051250, A089016 (largest n-round number).
%Y A122937 Sequence in context: A080197 A115847 A032966 this_sequence A060340 A078510 
               A017909
%Y A122937 Adjacent sequences: A122934 A122935 A122936 this_sequence A122938 A122939 
               A122940
%K A122937 fini,nonn
%O A122937 1,2
%A A122937 T. D. Noe (noe(AT)sspectra.com), Sep 21 2006

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