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

7,8

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

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 *)

Prog

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

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).

Sequence in context: A272863 A112632 A254575 * A275344 A206826 A175835

Adjacent sequences: A355399 A355400 A355401 * A355403 A355404 A355405

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jun 30 2022

Status

approved