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 A006446 Numbers n such that floor(sqrt(n)) divides n. (Formerly M0548) 20
 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 a(n) mod A000196(a(n)) = 0. - Reinhard Zumkeller, Apr 12 2013 Union of A000290, A002378, and A005563. - Fred Daniel Kline, Feb 06 2016 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 B. Cloitre, Some divisibility sequences 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. Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992. FORMULA For k>=1 a(3k-2)=k^2, a(3k-1)=k(k+1) and a(3k)=k(k+2). - Benoit Cloitre, Jan 14 2012 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. 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

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Last modified January 19 12:36 EST 2020. Contains 331049 sequences. (Running on oeis4.)