AMC 10B Fall 2021 (Problem 22)

Number TheoryHard

For each integer

n\ge2

, let

S_n

be the sum of all products

jk

, where

j

and

k

are integers and

1\le j<k\le n

. What is the sum of the

10

least values of

n

such that

S_n

is divisible by

3

\text{(A)}\;196

\text{(B)}\;197

\text{(C)}\;198

\text{(D)}\;199

\text{(E)}\;200