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
KEYWORD
nonn
AUTHOR
Alexander Kritov, Sep 23 2021
STATUS
approved