# 1770

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## Number

$1770$ (one thousand, seven hundred and seventy) is:

$2 \times 3 \times 5 \times 59$

The $30$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $703$, $780$, $861$, $946$, $1035$, $1225$, $1326$, $1431$, $1540$, $1653$:
$1770 = \ds \sum_{k \mathop = 1}^{30} \paren {4 k - 3} = 30 \paren {2 \times 30 - 1}$

The $59$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $1326$, $1378$, $1431$, $1485$, $1540$, $1596$, $1653$, $1711$:
$1770 = \ds \sum_{k \mathop = 1}^{59} k = \dfrac {59 \times \paren {59 + 1} } 2$