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Maximal GCD of three positive integers with sum n.
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%I #21 Sep 21 2022 11:28:28

%S 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,

%T 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,

%U 21,16,13,22,1,17,23,14,1,24,1,2,25,19,11,26,1,20,27,2,1,28

%N Maximal GCD of three positive integers with sum n.

%F From _Bernard Schott_, Jun 27 2022: (Start)

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

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

%t a[n_] := GCD @@@ IntegerPartitions[n, {3}] // Max;

%t Table[a[n], {n, 3, 100}] (* _Jean-François Alcover_, Sep 21 2022 *)

%o (Python)

%o from math import gcd

%o 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))

%o print([a(n) for n in range(3, 85)]) # _Michael S. Branicky_, Jun 26 2022

%Y Cf. A085891, A129648.

%Y 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).

%K nonn

%O 3,4

%A _Wesley Ivan Hurt_, Jun 25 2022