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Search: id:A006446
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| A006446 |
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Numbers n such that floor( sqrt n ) divides n.
(Formerly M0548)
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+0
7
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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; listen)
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OFFSET
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1,2
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COMMENT
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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
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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
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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.
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MAPLE
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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
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Select[ Range[ 500 ], Mod[ #, Floor[ Sqrt[ # ]//N ] ]==0& ]
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CROSSREFS
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Cf. A066377.
Cf. A035106, A087811.
Sequence in context: A122380 A033501 A097273 this_sequence A002348 A019469 A081491
Adjacent sequences: A006443 A006444 A006445 this_sequence A006447 A006448 A006449
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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