680

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Number

$680$ (six hundred and eighty) is:

$2^3 \times 5 \times 17$

The $2$nd tetrahedral number after $20$ which is the sum of two tetrahedral numbers:

$680 = 120 + 560$

The $15$th tetrahedral number, after $1$, $4$, $10$, $20$, $35$, $56$, $84$, $120$, $165$, $220$, $286$, $364$, $455$, $560$:

$680 = \ds \sum_{k \mathop = 1}^{15} \frac {k \paren {k + 1} } 2 = \dfrac {15 \paren {15 + 1} \paren {15 + 2} } 6$

Also see

• Previous  ... Next: Tetrahedral Numbers which are Sum of 2 Tetrahedral Numbers
• Previous  ... Next: Tetrahedral Number

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $680$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $680$