This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A347969 #38 Jan 27 2023 20:01:35 %S A347969 1715,6860,12635,15435,27440,42875,47915,50540,53235,61740,84035, %T A347969 109760,113715,138915,171500,191660,202160,207515,212940,218435, %U A347969 246960,289835,302715,315875,329315,336140,385875,415835,431235,439040,454860,479115,495635,555660,582435,619115,686000 %N A347969 Numbers which are sum of three squares of positive numbers and also 5 times of the sum of their joint products. %C A347969 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). %C A347969 For k=1 it is simply a(n) = 3*n^2 given by A033428. %C A347969 For k=2 it is A347360. %C A347969 The present sequence is for the next k=5. %C A347969 All possible k-numbers are listed by A331605. %D A347969 E. Grosswald, Representations of Integers as Sums of Squares, Springer-Verlag, NY, 1985. %e A347969 a(n) ( x, y, z) %e A347969 ------ ------------- %e A347969 1715 ( 3, 5, 41) %e A347969 6860 ( 6, 10, 82) %e A347969 12635 ( 5, 17, 111) %e A347969 15435 ( 9, 15, 123) %e A347969 27440 (12, 20, 164) %e A347969 42875 (15, 25, 205) %e A347969 47915 ( 3, 41, 215) %e A347969 50540 (10, 34, 222) %e A347969 53235 ( 5, 41, 227) %e A347969 61740 (18, 30, 246) %e A347969 84035 (21, 35, 287) %e A347969 109760 (24, 40, 328) %Y A347969 Cf. A000378, A033428, A331605 (all possible k-numbers), A347360. %K A347969 nonn %O A347969 1,1 %A A347969 _Alexander Kritov_, Sep 23 2021