4560

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Number

$4560$ (four thousand, five hundred and fifty-nine) is:

$2^4 \times 3 \times 5 \times 19$

The $48$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $3160$, $3321$, $3486$, $3655$, $3828$, $4005$, $4186$, $4371$:
$4560 = \ds \sum_{k \mathop = 1}^{48} \paren {4 k - 3} = 48 \paren {2 \times 48 - 1}$

The $95$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $3655$, $3741$, $3828$, $3916$, $4005$, $4095$, $4186$, $4278$, $4371$, $4465$:
$4560 = \ds \sum_{k \mathop = 1}^{95} k = \dfrac {95 \times \paren {95 + 1} } 2$