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A122936 2-Round numbers: numbers n such that every number less than n and relatively prime to n has at most two prime factors (counting multiplicities).

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%I A122936 #11 Feb 22 2020 06:36:41
%S A122936 1,2,3,4,5,6,7,8,10,12,14,16,18,20,22,24,26,30,36,42,48,54,60,66,72,
%T A122936 78,84,90,96,102,108,114,120,150,180,210,240,270,300,330,420,630,840,
%U A122936 1050,1260
%N A122936 2-Round numbers: numbers n such that every number less than n and relatively prime to n has at most two prime factors (counting multiplicities).
%C A122936 This sequence, for r=2 prime factors, is finite. Maillet proved that such sequences are finite for any fixed r. The case r=1 is A048597; case r=3 is A122937.
%D A122936 Dickson, History of the Theory of Numbers, Vol. I, Chelsea, New York, 1952, p. 134.
%H A122936 H. Bonse, <a href="https://archive.org/stream/archivdermathem31unkngoog#page/n307/mode/2up">Über eine bekannte Eigenshaft der Zahl 30 und ihre Verallgemeinerung</a>, Archiv d. Math. u. Physik (3) vol. 12 (1907) 292-295. See page 295.
%t A122936 Omega[n_] := If[n==1, 0, Plus@@(Transpose[FactorInteger[n]][[2]])]; nn=1260; r=2; 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
%t A122936 tpfQ[n_] :=Max[PrimeOmega /@ Select[Range[n - 1], CoprimeQ[#, n] &]] < 3; Select[Range[1300],tpfQ] (* _Harvey P. Dale_, Mar 16 2016 *)
%Y A122936 Cf. A048597 (very round numbers), A051250, A089016 (largest n-round number).
%K A122936 fini,full,nonn
%O A122936 1,2
%A A122936 _T. D. Noe_, Sep 21 2006