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).

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

Table of n, a(n) for n=1..45.

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

Adjacent sequences: A122933 A122934 A122935 * A122937 A122938 A122939

Keyword

fini,full,nonn

Author

T. D. Noe, Sep 21 2006

Status

approved