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A006446
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Numbers n such that floor(sqrt(n)) divides n.
(Formerly M0548)
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14
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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; internal format)
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OFFSET
| 1,2
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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 (maxale(AT)gmail.com), Nov 27 2006
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REFERENCES
| T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 73, problem 21.
S. W. Golomb, Problem E2491, Amer. Math. Monthly, 82 (1975), 854-855.
J. O. Shallit, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1..1000
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
B. Cloitre, Some divisibility sequences
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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
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MAPLE
| A006446:=(-1-z-z**2+z**3)/(z**2+z+1)**2/(z-1)**3; [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Select[ Range[ 500 ], Mod[ #, Floor[ Sqrt[ # ]//N ] ]==0& ]
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PROG
| (PARI) { n=0; for (m=1, 10^9, if (m%floor(sqrt(m)) == 0, write("b006446.txt", n++, " ", m); if (n==1000, return)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 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
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CROSSREFS
| Cf. A066377, A035106, A087811.
Sequence in context: A122380 A033501 A097273 * A002348 A019469 A081491
Adjacent sequences: A006443 A006444 A006445 * A006447 A006448 A006449
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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