The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A006446 Numbers k such that floor(sqrt(k)) divides k. (Formerly M0548) 25
 1, 2, 3, 4, 6, 8, 9, 12, 15, 16, 20, 24, 25, 30, 35, 36, 42, 48, 49, 56, 63, 64, 72, 80, 81, 90, 99, 100, 110, 120, 121, 132, 143, 144, 156, 168, 169, 182, 195, 196, 210, 224, 225, 240, 255, 256, 272, 288, 289, 306, 323, 324, 342, 360, 361, 380, 399, 400, 420 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numbers of the form k^2, k*(k+1), or k*(k+2). Nonsquare elements of this sequence are given by A035106. - Max Alekseyev, Nov 27 2006 Union of A000290, A002378, and A005563. - Fred Daniel Kline, Feb 06 2016 The asymptotic density of this sequence is 0 (Cooper and Kennedy, 1989). - Amiram Eldar, Jul 10 2020 REFERENCES T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 73, problem 21. Jeffrey Shallit, personal communication. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Harry J. Smith, Table of n, a(n) for n = 1..1000 Benoit Cloitre, Some divisibility sequences Curtis N. Cooper and Robert E. Kennedy, Chebyshev's inequality and natural density, Amer. Math. Monthly, Vol. 96, No. 2 (1989), pp. 118-124. S. W. Golomb, Problem E2491, Amer. Math. Monthly, 82 (1975), 854-855. Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009. Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992 Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1). FORMULA For k>=1 a(3*k-2) = k^2, a(3*k-1) = k*(k+1) and a(3*k) = k*(k+2). - Benoit Cloitre, Jan 14 2012 a(n) mod A000196(a(n)) = 0. - Reinhard Zumkeller, Apr 12 2013 a(n) = floor((n+1)/3)*(floor(n/3) + 1) +  floor((n+2)/3). - Ridouane Oudra, Nov 21 2020 a(n) = a(n-1) + 2*a(n-3) - 2*a(n-4) - a(n-6) + a(n-7) for n > 7. - Chai Wah Wu, Apr 05 2021 MAPLE A006446:=(-1-z-z**2+z**3)/(z**2+z+1)**2/(z-1)**3; # conjectured by Simon Plouffe in his 1992 dissertation A006446:=n->`if`(type(n/floor(sqrt(n)), integer), n, NULL); seq(A006446(n), n=1..100); # Wesley Ivan Hurt, Feb 11 2014 MATHEMATICA Select[ Range[ 500 ], Mod[ #, Floor[ Sqrt[ # ]//N ] ]==0& ] PROG (PARI) { n=0; for (m=1, 10^9, if (m%floor(sqrt(m)) == 0, write("b006446.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Feb 12 2010 (PARI) a(n)=my(k=n--\3+1); k*(k+n%3) \\ Charles R Greathouse IV, Jul 07 2011 (Haskell) a006446 n = a006446_list !! (n-1) a006446_list = filter (\x -> x `mod` a000196 x == 0) [1..] -- Reinhard Zumkeller, Mar 31 2011 CROSSREFS Cf. A000196, A035106, A066377, A087811. Sequence in context: A231404 A316860 A097273 * A261342 A002348 A019469 Adjacent sequences:  A006443 A006444 A006445 * A006447 A006448 A006449 KEYWORD nonn,easy,nice AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 3 05:09 EDT 2022. Contains 355030 sequences. (Running on oeis4.)