319

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Number

$319$ (three hundred and nineteen) is:

$11 \times 29$

The $4$th positive integer after $79$, $159$, $239$ which cannot be expressed as the sum of fewer than $19$ fourth powers:

$319 = 15 \times 1^4 + 3 \times 2^4 + 4^4$

or:

$319 = 12 \times 1^4 + 4 \times 2^4 + 3 \times 3^4$

The $12$th Smith number after $4$, $22$, $27$, $58$, $85$, $94$, $121$, $166$, $202$, $265$, $274$:

$3 + 1 + 9 = 1 + 1 + 2 + 9 = 13$

The $49$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $226$, $230$, $236$, $239$, $262$, $263$, $280$, $291$, $293$, $301$, $302$, $310$, $313$:

$319 \to 3^2 + 1^2 + 9^2 = 9 + 1 + 81 = 91 \to 9^2 + 1^2 = 81 + 1 = 82 \to 8^2 + 2^2 = 64 + 4 = 68 \to 6^2 + 8^2 = 36 + 64 = 100 \to 1^2 + 0^2 + 0^2 = 1$

Also see

• Previous  ... Next: Numbers not Expressible as Sum of Fewer than 19 Fourth Powers
• Previous  ... Next: Smith Number
• Previous  ... Next: Happy Number

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $319$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $319$