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%I #54 Aug 15 2022 04:30:41
%S 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,
%T 25,25,25,25,25,25,25,25,36,36,36,36,36,36,36,36,36,36,36,36,36,49,49,
%U 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
%N Largest square <= n.
%H Reinhard Zumkeller, <a href="/A048760/b048760.txt">Table of n, a(n) for n = 0..10000</a>
%H Krassimir T. Atanassov, <a href="http://www.gallup.unm.edu/~smarandache/Atanassov-SomeProblems.pdf">On Some of Smarandache's Problems</a>, 1999.
%H Henry Bottomley, <a href="/A000196/a000196.gif">Illustration of A000196, A048760, A053186</a>.
%H Jose Castillo, <a href="http://fs.unm.edu/FUNCT2.TXT">Other Smarandache Type Functions: Inferior/Superior Smarandache f-part of x</a>, Smarandache Notions Journal, Vol. 10, No. 1-2-3 (1999), pp. 202-204.
%H Valentina V. Radeva and Krassimir T. Atanassov, <a href="http://nntdm.net/volume-04-1998/number-3/101-104/">On the 40-th and 41-st Smarandache's problems</a>, Notes on Number Theory and Discrete Mathematics, Vol. 4, No. 3 (1998), pp. 101-104.
%H Florentin Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">Only Problems, Not Solutions!</a>, 1993.
%H Michael Somos, <a href="/A073189/a073189.txt">Sequences used for indexing triangular or square arrays</a>.
%F a(n) = floor(n^(1/2))^2 = A000290(A000196(n)). - _Reinhard Zumkeller_, Feb 12 2012, Sep 03 2002
%F n^2 repeated (2n+1) times, n=0,1,... - _Zak Seidov_, Oct 25 2008
%F Sum_{n>=1} (1/a(n) - 1/n) = gamma + zeta(2) (= A345202). - _Amiram Eldar_, Jun 12 2021
%F Sum_{n>=1} 1/a(n)^2 = 2*zeta(3) + Pi^4/90. - _Amiram Eldar_, Aug 15 2022
%p A048760 := proc(n)
%p floor(sqrt(n)) ;
%p %^2 ;
%p end proc: # _R. J. Mathar_, May 19 2016
%t Array[Floor[Sqrt[#]]^2&,80,0] (* _Harvey P. Dale_, Mar 30 2012 *)
%o (Haskell)
%o a048760 = (^ 2) . a000196 -- _Reinhard Zumkeller_, Feb 12 2012
%o (PARI) a(n) = sqrtint(n)^2; \\ _Michel Marcus_, Jun 06 2015
%Y Cf. A000196, A000290, A048761, A345202.
%K nonn,easy,look
%O 0,5
%A Charles T. Le (charlestle(AT)yahoo.com)
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