A355402 Maximal GCD of seven positive integers with sum n.

1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 1, 3, 1, 2, 3, 4, 1, 3, 1, 4, 3, 2, 5, 4, 1, 2, 3, 5, 1, 6, 1, 4, 5, 2, 1, 6, 7, 5, 3, 4, 1, 6, 5, 8, 3, 2, 1, 6, 1, 2, 9, 8, 5, 6, 1, 4, 3, 10, 1, 9, 1, 2, 5, 4, 11, 6, 1, 10, 9, 2, 1, 12, 5, 2, 3, 11, 1, 10, 13, 4, 3, 2, 5, 12

Offset: 7

Author

Wesley Ivan Hurt, Jun 30 2022

Keywords

• nonn
• easy

Comments

Also largest divisor <= n/7 of n. - David A. Corneth, Jul 24 2022

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..5000

Crossrefs

Cf. A009641, A355403.

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), this sequence (k=7), A354598 (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<7, 0, b(n$2, 7)):
seq(a(n), n=7..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 < 7, 0, b[n, n, 7]];
Table[a[n], {n, 7, 100}] (* Jean-François Alcover, Jul 24 2022, after Alois P. Heinz *)

PARI

a(n) = my(d = divisors(n)); d = select(x->x <= n\7,d); d[#d] \\ David A. Corneth, Jul 24 2022