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A007674
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Numbers n such that n and n+1 are squarefree.
(Formerly M1322)
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8
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1, 2, 5, 6, 10, 13, 14, 21, 22, 29, 30, 33, 34, 37, 38, 41, 42, 46, 57, 58, 61, 65, 66, 69, 70, 73, 77, 78, 82, 85, 86, 93, 94, 101, 102, 105, 106, 109, 110, 113, 114, 118, 122, 129, 130, 133, 137, 138, 141, 142, 145
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history;
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OFFSET
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1,2
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COMMENTS
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A008966(a(n))*A008966(a(n)+1) = 1. [Reinhard Zumkeller, Dec 03 2009]
n and n+1 squarefree implies n*(n+1) is squarefree oblong number, n*(n+1)/2 is squarefree triangular number. - Daniel Forgues, Aug 18 2012
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REFERENCES
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P. R. Halmos, Problems for Mathematicians Young and Old. Math. Assoc. America, 1991, p. 28.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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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a(n) = k*n, where k = 1/A065474. [Charles R Greathouse IV, Aug 10 2011]
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MATHEMATICA
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ff = {}; gg = {}; Do[kk = FactorInteger[n]; tak = False; Do[If[kk[[m]][[2]] > 1, tak = True], {m, 1, Length[kk]}]; If[tak == False, jj = FactorInteger[n + 1]; tak1 = False; Do[If[jj[[m]][[2]] > 1, tak1 = True], {m, 1, Length[jj]}]; If[tak1 == False, AppendTo[ff, n]]], {n, 1, 500}]; ff (* Artur Jasinski, Jan 28 2010 *)
Select[Range[400], SquareFreeQ[#(#+1)]&] (* Vladimir Joseph Stephan Orlovsky, Mar 30 2011 *)
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PROG
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(PARI) upTo(lim)=my(v=vectorsmall(floor(lim), i, 1), u=List()); for(n=2, sqrt(lim), forstep(i=n^2, lim, n^2, v[i]=v[i-1]=0)); for(i=1, lim, if(v[i], listput(u, i))); v=0; Vec(u) /* Charles R Greathouse IV, Aug 10 2011 */
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CROSSREFS
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A005117, A013929, A172186, A172187 [From Artur Jasinski, Jan 28 2010]
Sequence in context: A212015 A089269 A047440 * A086719 A115200 A075823
Adjacent sequences: A007671 A007672 A007673 * A007675 A007676 A007677
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KEYWORD
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nonn,easy,changed
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AUTHOR
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N. J. A. Sloane, Robert G. Wilson v
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EXTENSIONS
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Initial 1 added at suggestion of Zak Seidov, Sep 19 2007
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STATUS
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approved
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