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A354599 Maximal GCD of nine positive integers with sum n.

%I A354599 #20 Sep 21 2022 10:39:35
%S A354599 1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,2,3,2,1,3,1,2,3,2,1,4,1,2,3,4,1,3,
%T A354599 1,4,5,2,1,4,1,5,3,4,1,6,5,4,3,2,1,6,1,2,7,4,5,6,1,4,3,7,1,8,1,2,5,4,
%U A354599 7,6,1,8,9,2,1,7,5,2,3,8,1,10,7,4,3,2,5,8,1,7,11,10
%N A354599 Maximal GCD of nine positive integers with sum n.
%p A354599 b:= proc(n, i, t) option remember; `if`(n=0, signum(t),
%p A354599      `if`(min(i, t)<1, 1, max(b(n, i-1, t),
%p A354599       igcd(b(n-i, min(n-i, i), t-1), i))))
%p A354599     end:
%p A354599 a:= n-> `if`(n<9, 0, b(n$2, 9)):
%p A354599 seq(a(n), n=9..200);  # _Alois P. Heinz_, Jul 13 2022
%t A354599 b[n_, i_, t_] := b[n, i, t] = If[n == 0, Sign[t], If[Min[i, t] < 1, 1, Max[b[n, i - 1, t], GCD[b[n - i, Min[n - i, i], t - 1], i]]]];
%t A354599 a[n_] := If[n < 9, 0, b[n, n, 9]];
%t A354599 Table[a[n], {n, 9, 100}] (* _Jean-François Alcover_, Sep 21 2022, after _Alois P. Heinz_ *)
%Y A354599 Cf. A009714.
%Y A354599 Maximal GCD of k positive integers with sum n for k = 2..10: A032742 (k=2,n>=2), A355249 (k=3), A355319 (k=4), A355366 (k=5), A355368 (k=6), A355402 (k=7), A354598 (k=8), this sequence (k=9), A354601 (k=10).
%K A354599 nonn
%O A354599 9,10
%A A354599 _Wesley Ivan Hurt_, Jul 08 2022