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a(n) is the greatest square of the form floor(n/k) where k > 0.
2

%I #9 Feb 05 2020 05:42:47

%S 0,1,1,1,4,1,1,1,4,9,1,1,4,4,4,1,16,4,9,9,4,4,4,4,4,25,4,9,9,9,4,4,16,

%T 16,4,4,36,9,9,9,4,4,4,4,4,9,9,9,16,49,25,25,4,4,9,9,9,9,9,9,4,4,4,9,

%U 64,16,16,16,9,9,4,4,36,36,9,25,25,25,9,9,16

%N a(n) is the greatest square of the form floor(n/k) where k > 0.

%H Rémy Sigrist, <a href="/A332012/b332012.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A331958(n)^2.

%F a(n^2) = n^2.

%F a(2*n^2) = n^2.

%e For n = 8:

%e - floor(8/1) = 8 is not a square number,

%e - floor(8/2) = 4 is a square number,

%e - hence a(8) = 4.

%o (PARI) a(n) = for (k=1, oo, if (issquare(n\k), return (n\k)))

%Y Cf. A331953, A331958.

%K nonn

%O 0,5

%A _Rémy Sigrist_, Feb 04 2020