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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).
2
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, 78, 84, 90, 96, 102, 108, 114, 120, 150, 180, 210, 240, 270, 300, 330, 420, 630, 840, 1050, 1260
OFFSET
1,2
COMMENTS
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.
REFERENCES
Dickson, History of the Theory of Numbers, Vol. I, Chelsea, New York, 1952, p. 134.
LINKS
H. Bonse, Über eine bekannte Eigenshaft der Zahl 30 und ihre Verallgemeinerung, Archiv d. Math. u. Physik (3) vol. 12 (1907) 292-295. See page 295.
MATHEMATICA
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
tpfQ[n_] :=Max[PrimeOmega /@ Select[Range[n - 1], CoprimeQ[#, n] &]] < 3; Select[Range[1300], tpfQ] (* Harvey P. Dale, Mar 16 2016 *)
CROSSREFS
Cf. A048597 (very round numbers), A051250, A089016 (largest n-round number).
Sequence in context: A032958 A080750 A113768 * A330729 A118729 A008726
KEYWORD
fini,full,nonn
AUTHOR
T. D. Noe, Sep 21 2006
STATUS
approved