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Search: id:A122937
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| A122937 |
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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). |
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+0
3
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| 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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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REFERENCES
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Dickson, History of the Theory of Numbers, Vol. I, Chelsea, New York, 1952, p. 134.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..265 [complete list]
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MATHEMATICA
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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
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CROSSREFS
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Cf. A048597 (very round numbers), A051250, A089016 (largest n-round number).
Sequence in context: A080197 A115847 A032966 this_sequence A060340 A078510 A017909
Adjacent sequences: A122934 A122935 A122936 this_sequence A122938 A122939 A122940
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KEYWORD
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fini,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Sep 21 2006
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