# 4753

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## Number

$4753$ (four thousand, seven hundred and fifty-three) is:

$7^2 \times 97$

The $49$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $3160$, $3321$, $3486$, $3655$, $3828$, $4005$, $4186$, $4371$, $4560$:
$4753 = \ds \sum_{k \mathop = 1}^{49} \paren {4 k - 3} = 49 \paren {2 \times 49 - 1}$

The $97$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $4095$, $4186$, $4278$, $4371$, $4465$, $4560$, $4656$:
$4753 = \ds \sum_{k \mathop = 1}^{97} k = \dfrac {97 \times \paren {97 + 1} } 2$