A355249 Maximal GCD of three positive integers with sum n.

1, 1, 1, 2, 1, 2, 3, 2, 1, 4, 1, 2, 5, 4, 1, 6, 1, 5, 7, 2, 1, 8, 5, 2, 9, 7, 1, 10, 1, 8, 11, 2, 7, 12, 1, 2, 13, 10, 1, 14, 1, 11, 15, 2, 1, 16, 7, 10, 17, 13, 1, 18, 11, 14, 19, 2, 1, 20, 1, 2, 21, 16, 13, 22, 1, 17, 23, 14, 1, 24, 1, 2, 25, 19, 11, 26, 1, 20, 27, 2, 1, 28

Offset

3,4

Links

Table of n, a(n) for n=3..84.

Formula

From Bernard Schott, Jun 27 2022: (Start)

a(3n) = n for n >= 1.

a(p) = 1 for p prime >= 3. (End)

Mathematica

a[n_] := GCD @@@ IntegerPartitions[n, {3}] // Max;
Table[a[n], {n, 3, 100}] (* Jean-François Alcover, Sep 21 2022 *)

Prog

(Python)
from math import gcd
def a(n): return max(gcd(i, j, n-i-j) for i in range(1, n//3+1) for j in range(i, n//3+1))
print([a(n) for n in range(3, 85)]) # Michael S. Branicky, Jun 26 2022

Crossrefs

Cf. A085891, A129648.

Maximal GCD of k positive integers with sum n for k = 2..10: A032742 (k=2,n>=2), this sequence (k=3), A355319 (k=4), A355366 (k=5), A355368 (k=6), A355402 (k=7), A354598 (k=8), A354599 (k=9), A354601 (k=10).

Sequence in context: A134388 A055095 A366770 * A337618 A048685 A364663

Adjacent sequences: A355246 A355247 A355248 * A355250 A355251 A355252

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 25 2022

Status

approved