import math

MOD = 998244353

# Index * A Problem の答えの上界
LIMIT = 42

LCM = [0] + [math.lcm(*range(1, i + 1)) for i in range(1, LIMIT + 2)]
inv_2 = pow(2, MOD - 2, MOD)


def solve(N):
    def count(ans):
        loop = N // LCM[ans]
        res = LCM[ans] // ans * ((N + 1) * loop - loop * (loop + 1) * inv_2 * LCM[ans]) % MOD
        return res

    answer = 0

    for i in range(1, LIMIT + 1):
        answer += (count(i) - count(i + 1)) * i
        answer %= MOD

    return answer


# def normal(L, R):
#     for i in range(LIMIT, 0, -1):
#         lcm = math.lcm(*range(1, i + 1))

#         min_val = lcm // i
#         d = (L + min_val - 1) // min_val

#         if lcm * d > R:
#             continue

#         A = [lcm * d // j for j in range(1, i + 1)]
#         assert len({a * i for i, a in enumerate(A, start=1)}) == 1
#         return i


if __name__ == "__main__":
    T = int(input())
    for _ in range(T):
        N = int(input())
        print(solve(N))

        # assert solve(N) == sum(sum(normal(l, r) for r in range(l, N + 1)) for l in range(1, N + 1)) % MOD