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A347969
Numbers which are sum of three squares of positive numbers and also 5 times of the sum of their joint products.
1
1715, 6860, 12635, 15435, 27440, 42875, 47915, 50540, 53235, 61740, 84035, 109760, 113715, 138915, 171500, 191660, 202160, 207515, 212940, 218435, 246960, 289835, 302715, 315875, 329315, 336140, 385875, 415835, 431235, 439040, 454860, 479115, 495635, 555660, 582435, 619115, 686000
OFFSET
1,1
COMMENTS
The general problem is to find such numbers which can be represented as the sum of three squares of integers x, y, z, and additionally also satisfy: x^2 + y^2 + z^2 = k*(x*y + x*z + y*z).
For k=1 it is simply a(n) = 3*n^2 given by A033428.
For k=2 it is A347360.
The present sequence is for the next k=5.
All possible k-numbers are listed by A331605.
REFERENCES
E. Grosswald, Representations of Integers as Sums of Squares, Springer-Verlag, NY, 1985.
EXAMPLE
a(n) ( x, y, z)
------ -------------
1715 ( 3, 5, 41)
6860 ( 6, 10, 82)
12635 ( 5, 17, 111)
15435 ( 9, 15, 123)
27440 (12, 20, 164)
42875 (15, 25, 205)
47915 ( 3, 41, 215)
50540 (10, 34, 222)
53235 ( 5, 41, 227)
61740 (18, 30, 246)
84035 (21, 35, 287)
109760 (24, 40, 328)
CROSSREFS
Cf. A000378, A033428, A331605 (all possible k-numbers), A347360.
Sequence in context: A184090 A297560 A157247 * A267201 A024408 A267741
KEYWORD
nonn
AUTHOR
Alexander Kritov, Sep 23 2021
STATUS
approved