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%I #17 Feb 05 2021 04:39:39
%S 0,1,2,8,20,44,140,320,476,3584,12311,4604,74879,414119,2071775,
%T 5703551,11551671,45680444,442548224,1960632176,2657058876,
%U 24923993276,130518272975,1478154932316,5446454455004,38610655379975
%N Smallest number k such that n! - k is a square
%C Sequence is not monotonic: a(n) < a(n-1) for n = 12, 71, 90, 143, 145, 151, 172, 218, 257. - _Zak Seidov_, Jun 25 2013
%H T. D. Noe, <a href="/A066857/b066857.txt">Table of n, a(n) for n = 1..100</a>
%F a(n) = A053186(n!) = n!-A048760(n!) = n!-floor(sqrt(n!))^2 = n!-A055226(n)^2.
%e a(10) = 3628800 - 1904 * 1904 = 3628800 - 3625216 = 3584.
%t Table[n! - Floor[Sqrt[n! ]]^2, {n, 1, 27}]
%o (PARI) a(n)=my(N=n!); N-sqrtint(N)^2 \\ _Charles R Greathouse IV_, Jun 25 2013
%Y Cf. A068869.
%K nonn
%O 1,3
%A _Reinhard Zumkeller_, Jan 21 2002
%E More terms from _Vladeta Jovovic_, Mar 21 2002
%E Edited by _Robert G. Wilson v_ and _N. J. A. Sloane_, Mar 22 2002
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