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%I A036465 #27 May 08 2022 09:21:24
%S A036465 1,1,2,3,3,2,4,4,6,6,6,5,7,9,8,8,9,8,12,8,12,8,12,15,13,12,14,20,18,
%T A036465 14,16,18,17,21,18,14,19,19,24,23,21,18,24,27,23,20,24,23,30,24,26,28,
%U A036465 27,33,28,28,40,30,36,28,31,34,32,39,36,31,34,35,42,30
%N A036465 If n^2 = Sum_{i} b(i)^2 for positive integers b(i) < n, then a(n) is the maximum value of min(b(i)).
%H A036465 Alois P. Heinz, <a href="/A036465/b036465.txt">Table of n, a(n) for n = 2..800</a>
%e A036465 a(9) = 4 since 9^2 = 7^2 + 4^2 + 4^2.
%p A036465 b:= proc(n, i) option remember; (s-> `if`(i=1, 1,
%p A036465       `if`(s>=n and issqr(n), isqrt(n), max(
%p A036465       `if`(s>n, 0, b(n-s, i)), b(n, i-1)))))(i^2)
%p A036465     end:
%p A036465 a:= n-> b(n^2, n-1):
%p A036465 seq(a(n), n=2..75);  # _Alois P. Heinz_, Nov 03 2020
%t A036465 b[n_, i_] := b[n, i] = Function[s, If[i == 1, 1,
%t A036465      If[s >= n && IntegerQ@Sqrt[n], Sqrt[n], Max[
%t A036465      If[s > n, 0, b[n-s, i]], b[n, i-1]]]]][i^2];
%t A036465 a[n_] := b[n^2, n-1];
%t A036465 Table[a[n], {n, 2, 75}] (* _Jean-François Alcover_, May 08 2022, after _Alois P. Heinz_ *)
%K A036465 nonn
%O A036465 2,3
%A A036465 _Erich Friedman_
%E A036465 Title improved by _Sean A. Irvine_, Nov 03 2020

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