There are 5 statistics on Cores in the database:
(and possibly some waiting for verification)

St000158Cores ⟶ ℤ
The length of a core.
St000190Cores ⟶ ℤ
The size of a core.
St000191Cores ⟶ ℤ
The number of strong covers of a core.
St000192Cores ⟶ ℤ
Number of covers of a core in weak Bruhat order.
St000202Cores ⟶ ℤ
The number of k-cores contained in the k-core.