A354599 Maximal GCD of nine positive integers with sum n.

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

Offset

9,10

Links

Table of n, a(n) for n=9..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<9, 0, b(n$2, 9)):
seq(a(n), n=9..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 < 9, 0, b[n, n, 9]];
Table[a[n], {n, 9, 100}] (* Jean-François Alcover, Sep 21 2022, after Alois P. Heinz *)

Crossrefs

Cf. A009714.

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).

Sequence in context: A167969 A245192 A235431 * A303536 A259656 A096370

Adjacent sequences: A354596 A354597 A354598 * A354600 A354601 A354602

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 08 2022

Status

approved