Numbers Not Expressible as Sum of no more than 5 Squares of Composite Numbers

Theorem

There are $256$ integers which cannot be expressed as the sum of no more than $5$ squares of composite numbers:

$1, 2, 3, \ldots, 1167$

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Sources

• 1994: Richard K. Guy: Unsolved Problems in Number Theory (2nd ed.): $\mathbf C$: Additive Number Theory: $\mathbf {C 20}$: Sums of Squares
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1167$