Integer as Sum of Three Squares/Sequence

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The sequence of positive integers that cannot be expressed as the sum of at most $3$ squares begins:

$7, 15, 23, 28, 31, 39, 47, 55, 60, \ldots$

This sequence is A004215 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).