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A374059
a(n) is the smallest integer k such that k*x*y*z = (x + k) * (y + k) * (z + k), 0 < x <= y <= z has exactly n integer solutions.
1
1, 11, 13, 25, 7, 9, 22, 48, 5, 21, 14, 8, 280, 10, 1020, 4, 70, 3, 6, 240, 2, 42, 12, 660, 30
OFFSET
0,2
COMMENTS
a(27)=630, a(29)=60, a(30)=420. No solutions were found for n={25,26,28} with k<10^5.
EXAMPLE
For n=8, a(n)=5 because 5 is the smallest integer such that 5*x*y*z = (x+5)*(y+5)*(z+5), 0 < x <= y <= z has exactly 8 positive integer solutions: {{2,12,595}, {2,14,95}, {2,15,70}, {2,20,35}, {3,6,220}, {3,10,20}, {4,5,45}, {5,5,20}}.
CROSSREFS
Cf. A375787.
Sequence in context: A277048 A275598 A090433 * A022325 A295340 A153055
KEYWORD
nonn,more
AUTHOR
Zhining Yang, Oct 28 2024
EXTENSIONS
a(12) corrected by Jinyuan Wang, Dec 04 2024
STATUS
approved