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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 30 07:19 EST 2023. Contains 359939 sequences. (Running on oeis4.)