2080
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Number
$2080$ (two thousand and eighty) is:
- $2^5 \times 5 \times 13$
- The total of all the entries in a magic cube of order $4$, after $1$, $36$, $378$:
- $2080 = \ds \sum_{k \mathop = 1}^{4^3} k = \dfrac {4^3 \paren {4^3 + 1} } 2$
- The total of all the entries in a magic square of order $8$, after $1$, $(10)$, $45$, $136$, $325$, $666$, $1225$:
- $2080 = \ds \sum_{k \mathop = 1}^{8^2} k = \dfrac {8^2 \paren {8^2 + 1} } 2$
- The $64$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $1326$, $1378$, $1431$, $1485$, $1540$, $1596$, $1653$, $1711$, $1770$, $1770$, $1830$, $1891$, $1953$, $2016$:
- $2080 = \ds \sum_{k \mathop = 1}^{64} k = \dfrac {64 \times \paren {64 + 1} } 2$