# 2556

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## Number

$2556$ (two thousand, five hundred and fifty-six) is:

$2^2 \times 3^2 \times 71$

The largest term of the amicable triplet $\tuple {1980, 2016, 2556}$:
$\map {\sigma_1} {1980} = \map {\sigma_1} {2016} = \map {\sigma_1} {2556} = 6552 = 1980 + 2016 + 2556$

The $36$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $1431$, $1540$, $1653$, $1770$, $1891$, $2016$, $2145$, $2278$, $2415$:
$2556 = \ds \sum_{k \mathop = 1}^{36} \paren {4 k - 3} = 36 \paren {2 \times 35 - 1}$

The $71$st triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $1891$, $1953$, $2016$, $2080$, $2145$, $2211$, $2278$, $2346$, $2415$, $2485$:
$2556 = \ds \sum_{k \mathop = 1}^{71} k = \dfrac {71 \times \paren {71 + 1} } 2$