5460
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Number
$5460$ (five thousand, four hundred and sixty) is:
- $2^2 \times 3 \times 5 \times 7 \times 13$
- The $1$st of the $7$th pair of triangular numbers whose sum and difference are also both triangular:
- $5460 = T_{104}$, $6786 = T_{116}$, $6786 + 5460 = T_{156}$, $6786 - 5460 = T_{51}$
- The $104$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $4560$, $4656$, $4753$, $4851$, $4950$, $5050$, $5151$, $5253$, $5356$:
- $5460 = \ds \sum_{k \mathop = 1}^{104} k = \dfrac {104 \times \paren {104 + 1} } 2$