login
This site is supported by donations to The OEIS Foundation.
Logo

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A007674 Numbers n such that n and n+1 are squarefree.
(Formerly M1322)
8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

REFERENCES

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).

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

FORMULA

a(n) = k*n, where k = 1/A065474. [Charles R Greathouse IV, Aug 10 2011]

MATHEMATICA

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 *)

PROG

(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 */

CROSSREFS

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

KEYWORD

nonn,easy,changed

AUTHOR

N. J. A. Sloane, Robert G. Wilson v

EXTENSIONS

Initial 1 added at suggestion of Zak Seidov, Sep 19 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified May 23 21:50 EDT 2013. Contains 225612 sequences.