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).

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, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192

Offset: 1

Author

T. D. Noe, Sep 21 2006

Keywords

• fini
• full
• nonn

Comments

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.

References

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

Links

• T. D. Noe, Table of n, a(n) for n=1..265 (complete sequence)

Crossrefs

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

Programs

Mathematica

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