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A048760
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Largest square <= n.
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48
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0, 1, 1, 1, 4, 4, 4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 16, 16, 16, 16, 16, 16, 16, 16, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Krassimir T. Atanassov, On Some of Smarandache's Problems, 1999.
Henry Bottomley, Illustration of A000196, A048760, A053186.
Jose Castillo, Other Smarandache Type Functions: Inferior/Superior Smarandache f-part of x, Smarandache Notions Journal, Vol. 10, No. 1-2-3 (1999), pp. 202-204.
Valentina V. Radeva and Krassimir T. Atanassov, On the 40-th and 41-st Smarandache's problems, Notes on Number Theory and Discrete Mathematics, Vol. 4, No. 3 (1998), pp. 101-104.
Florentin Smarandache, Only Problems, Not Solutions!, 1993.
Michael Somos, Sequences used for indexing triangular or square arrays.
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FORMULA
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a(n) = floor(n^(1/2))^2 = A000290(A000196(n)). - Reinhard Zumkeller, Feb 12 2012, Sep 03 2002
n^2 repeated (2n+1) times, n=0,1,... - Zak Seidov, Oct 25 2008
Sum_{n>=1} (1/a(n) - 1/n) = gamma + zeta(2) (= A345202). - Amiram Eldar, Jun 12 2021
Sum_{n>=1} 1/a(n)^2 = 2*zeta(3) + Pi^4/90. - Amiram Eldar, Aug 15 2022
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MAPLE
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A048760 := proc(n)
floor(sqrt(n)) ;
%^2 ;
end proc: # R. J. Mathar, May 19 2016
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MATHEMATICA
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Array[Floor[Sqrt[#]]^2&, 80, 0] (* Harvey P. Dale, Mar 30 2012 *)
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PROG
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(Haskell)
a048760 = (^ 2) . a000196 -- Reinhard Zumkeller, Feb 12 2012
(PARI) a(n) = sqrtint(n)^2; \\ Michel Marcus, Jun 06 2015
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CROSSREFS
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Cf. A000196, A000290, A048761, A345202.
Sequence in context: A108893 A162281 A262690 * A287392 A035627 A228423
Adjacent sequences: A048757 A048758 A048759 * A048761 A048762 A048763
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KEYWORD
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nonn,easy,look
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AUTHOR
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Charles T. Le (charlestle(AT)yahoo.com)
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STATUS
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approved
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