Primes:
$2020 = 17 ^ 2 + 19 ^ 2 + 23 ^ 2 + 29 ^ 2$ is the sum of four consecutive prime.
$2020 = 2 + 3 + 7 + 8 + 11 + 12 + 15 + 18 + 26 + 27 + 28 + 29 + 34 + 35 + 38 + 40 + 42 + 46 + 48 + 50 + 51 + 53 + 55 + 59 + 61 + 63 + 66 + 67 + 72 + 73 + 74 + 75 + 83 + 86 + 89 + 90 + 93 + 94 + 98 + 99$ is the sum of all primitive roots of $101$.
$2020 = p_{14}p_{15}-1$.
Counting:
$2020$ is the number of partition of $48$ into distinct parts $\neq7$.
Other:
$2020 = \left[\sqrt{21 ^ 5}\right]$.