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

8,9

Links

Table of n, a(n) for n=8..100.

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 *)

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).

Sequence in context: A323880 A338651 A033107 * A239061 A309025 A247599

Adjacent sequences: A354595 A354596 A354597 * A354599 A354600 A354601

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 08 2022

Status

approved