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

1,2

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)

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

Crossrefs

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

Sequence in context: A115847 A204315 A032966 * A246076 A246082 A060340

Adjacent sequences: A122934 A122935 A122936 * A122938 A122939 A122940

Keyword

fini,full,nonn

Author

T. D. Noe, Sep 21 2006

Status

approved