A354598 Maximal GCD of eight positive integers with sum n.

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 3, 2, 1, 3, 1, 4, 3, 2, 1, 4, 1, 2, 3, 5, 1, 3, 1, 4, 5, 2, 1, 6, 1, 5, 3, 4, 1, 6, 5, 7, 3, 2, 1, 6, 1, 2, 7, 8, 5, 6, 1, 4, 3, 7, 1, 9, 1, 2, 5, 4, 7, 6, 1, 10, 9, 2, 1, 7, 5, 2, 3, 11, 1, 10, 7, 4, 3, 2, 5, 12, 1, 7, 11, 10

Offset: 8

Author

Wesley Ivan Hurt, Jul 08 2022

Keywords

• nonn

Crossrefs

Cf. A009694, A162787.

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), this sequence (k=8), A354599 (k=9), A354601 (k=10).

Programs

Maple

b:= proc(n, i, t) option remember; `if`(n=0, signum(t),
     `if`(min(i, t)<1, 1, max(b(n, i-1, t),
      igcd(b(n-i, min(n-i, i), t-1), i))))
    end:
a:= n-> `if`(n<8, 0, b(n$2, 8)):
seq(a(n), n=8..200);  # Alois P. Heinz, Jul 13 2022

Mathematica

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]]]];
a[n_] := If[n < 8, 0, b[n, n, 8]];
Table[a[n], {n, 8, 100}] (* Jean-François Alcover, Sep 21 2022, after Alois P. Heinz *)