A274255 Numbers n such that n^2 is the sum of three nonzero squares while n is not.
7, 13, 15, 23, 25, 28, 31, 37, 39, 47, 52, 55, 58, 60, 63, 71, 79, 85, 87, 92, 95, 100, 103, 111, 112, 119, 124, 127, 130, 135, 143, 148, 151, 156, 159, 167, 175, 183, 188, 191, 199, 207, 208, 215, 220, 223, 231, 232, 239, 240, 247, 252, 255, 263, 271, 279, 284
Offset: 1
Examples
7 is a term because 7 is not in A000408 and 7^2 = 49 = 2^2 + 3^2 + 6^2.