[math-fun] 1,409, 481, 24961, 28721, ...?

*Very* probably spotty list: 1,409, 481, 24961, 28721, 65441, 113241, 121609, 345761, 362401, 384161, 530881, 620321, 854401, 882889, 909321, 1163249,... the squarefree part of integers of the form √(a⁴+b⁴+c⁴). Like the congruent numbers, you can't rule them out with finite searching. 1 doesn't show up until a=414560, b=217519, c=95800 (https://en.wikipedia.org/wiki/Euler%27s_sum_of_powers_conjecture). Are there really none with four digits? Two? —rwg