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Search: id:A007675
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| A007675 |
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Numbers n such that n, n+1 and n+2 are square-free.
(Formerly M3824)
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+0
10
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| 1, 5, 13, 21, 29, 33, 37, 41, 57, 65, 69, 77, 85, 93, 101, 105, 109, 113, 129, 137, 141, 157, 165, 177, 181, 185, 193, 201, 209, 213, 217, 221, 229, 237, 253, 257, 265, 281, 285, 301, 309, 317, 321, 329, 345
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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There can not be four consecutive square-free numbers as one of them is divisible by 2^2 =4. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 18 2002
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
P. R. Halmos, Problems for Mathematicians Young and Old. Math. Assoc. America, 1991, p. 28.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
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FORMULA
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m(x)*m(x+1)*m(x+2)=1, where m(w)=Abs(mu(w)). - Labos E. (labos(AT)ana.sote.hu)
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EXAMPLE
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4 categories: all terms are composites like {33,34,35}; first term only is prime like {37,38,39}; 3rd term only is prime like {57,58,59}; first and 3rd are primes like {29,30,31}. - Labos E. (labos(AT)ana.sote.hu)
85 is a term as 85 = 17*5, 86 = 43*2, 87 = 29*3.
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MATHEMATICA
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f[n_]:=Union[Last/@FactorInteger[n]][[ -1]]; lst={1}; Do[If[f[n]==1&&f[n+1]==1&&f[n+2]==1, AppendTo[lst, n]], {n, 2, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 07 2010]
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CROSSREFS
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Sequence in context: A087714 A055045 A030374 this_sequence A043441 A004770 A107996
Adjacent sequences: A007672 A007673 A007674 this_sequence A007676 A007677 A007678
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KEYWORD
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nonn,easy,nice,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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