A001948 These numbers when multiplied by all powers of 4 give the numbers [ up to 160000 ] that are not the sums of 4 distinct squares.

1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 15, 17, 18, 19, 22, 23, 25, 27, 31, 33, 34, 37, 43, 47, 55, 58, 67, 73, 82, 97, 103