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

Author

Wesley Ivan Hurt, Jun 25 2022

Keywords

• nonn

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).

Programs

Mathematica

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

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

Formula

From Bernard Schott, Jun 27 2022: (Start)

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

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