# 2016

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## Number

$2016$ (two thousand and sixteen) is:

$2^5 \times 3^2 \times 7$

The $2$nd number after $360$ whose ratio to aliquot sum is $4 : 9$:
$\dfrac {\map \sigma {2016} - 2016} {2016} = \dfrac 9 4$
where $\sigma$ denotes the $\sigma$ (sigma) function.

The $9$th positive integer after $504$, $756$, $806$, $1008$, $1148$, $1209$, $1472$, $1512$ which can be expressed as the product of $2$ two-digit numbers in $2$ ways such that the factors in one of those pairs is the reversal of each of the factors in the other:
$2016 = 24 \times 84 = 48 \times 42$

The $32$nd hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $703$, $780$, $861$, $946$, $1035$, $1225$, $1326$, $1431$, $1540$, $1653$, $1770$, $1891$:
$2016 = \displaystyle \sum_{k \mathop = 1}^{32} \paren {4 k - 3} = 32 \paren {2 \times 32 - 1}$

The $63$rd triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $1326$, $1378$, $1431$, $1485$, $1540$, $1596$, $1653$, $1711$, $1770$, $1770$, $1830$, $1891$, $1953$:
$2016 = \displaystyle \sum_{k \mathop = 1}^{63} k = \dfrac {63 \times \paren {63 + 1} } 2$

$2016 = 3^3 + 4^3 + 5^3 + 6^3 + 7^3 + 8^3 + 9^3$

The $\sigma$ (sigma) value of $672$:
$\map \sigma {672} = 2016 = 3 \times 672$

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