# 3655

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## 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:
$\map {\sigma_0} {3655} = \map {\sigma_0} {3656} = \map {\sigma_0} {3657} = \map {\sigma_0} {3658} = 8$

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

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