STATUS
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proposed
b[n_, i_] := b[n, i] = Function[s, If[i == 1, 1,
If[s >= n && IntegerQ@Sqrt[n], Sqrt[n], Max[
If[s > n, 0, b[n-s, i]], b[n, i-1]]]]][i^2];
a[n_] := b[n^2, n-1];
Table[a[n], {n, 2, 75}] (* Jean-François Alcover, May 08 2022, after Alois P. Heinz *)
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Alois P. Heinz, <a href="/A036465/b036465_3.txt">Table of n, a(n) for n = 2..800</a>
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Alois P. Heinz, <a href="/A036465/b036465_3.txt">Table of n, a(n) for n = 2..700800</a>
approved
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Alois P. Heinz, <a href="/A036465/b036465_2.txt">Table of n, a(n) for n = 2..700</a>
editing
approved
Alois P. Heinz, <a href="/A036465/b036465_2.txt">Table of n, a(n) for n = 2..600700</a>
approved
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Alois P. Heinz, <a href="/A036465/b036465_1.txt">Table of n, a(n) for n = 2..600</a>