T = int(input())

def gcd(a, b):
	if b == 0:
		return a
	else:
		return gcd(b, a % b)

MOD = 998244353
for _ in range(T):
	N = int(input())
	lcm = 1
	ans = (N * (N + 1) // 2) % MOD
	for i in range(2, 50):
		lcm = (lcm * i) // gcd(lcm, i)
		if lcm > N:
			break
		K = (N ) // lcm
		m = ((lcm ** 2 // i) * ((K * (K + 1)) // 2)) % MOD
		t = ((K * lcm) // i) % MOD
		m = (m - t * ((K + 1) * lcm - 1 - N)) % MOD
		#print(i, lcm, m, K)
		ans = (ans + m) % MOD
	print(ans)