3655

Number
$3655$ (three thousand, six hundred and fifty-five) is:


 * $5 \times 17 \times 43$


 * The $1$st of the $2$nd quadruple of consecutive integers which all have an equal divisors:
 * $\map \tau {3655} = \map \tau {3656} = \map \tau {3657} = \map \tau {3658} = 8$


 * The $43$rd hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $2145$, $2278$, $2415$, $2556$, $2701$, $2850$, $3003$, $3160$, $3321$, $3486$:
 * $3655 = \displaystyle \sum_{k \mathop = 1}^{43} \paren {4 k - 3} = 43 \paren {2 \times 43 - 1}$


 * The $85$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $2701$, $2775$, $2850$, $2926$, $3003$, $3081$, $3160$, $3240$, $3321$, $3403$, $3486$, $3570$:
 * $3655 = \displaystyle \sum_{k \mathop = 1}^{85} k = \dfrac {85 \times \paren {85 + 1} } 2$