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Consider the positive squares summing to n as obtained by the greedy algorithm; a(n) is the least of these squares.
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%I #6 Jan 24 2022 16:12:46

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

%T 9,1,36,1,1,1,4,1,1,1,4,9,1,1,1,49,1,1,1,4,1,1,1,4,9,1,1,1,4,1,64,1,1,

%U 1,4,1,1,1,4,9,1,1,1,4,1,1,16,81,1,1,1

%N Consider the positive squares summing to n as obtained by the greedy algorithm; a(n) is the least of these squares.

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

%F a(n) = A350674(n, A053610(n)).

%e For n = 13:

%e - 13 = 3^2 + 2^2,

%e - so a(13) = 2^2.

%o (PARI) a(n, e=2) = { my (r=0); while (n, r=sqrtnint(n, e); n-=r^e); r^e }

%Y Cf. A053610, A350674.

%K nonn

%O 1,4

%A _Rémy Sigrist_, Jan 12 2022