Counting Divisors (cube)

Let σ0(n) be the number of positive divisors of n

.

For example, σ0(1)=1

, σ0(2)=2 and σ0(6)=4

.

Let

S3(n)=∑i=1nσ0(i3).

First line of Input contains T (1≤T≤10000

), the number of test cases.

Next T

lines contain a single number N. (1≤N≤1011)

For each number N, output a single line containing S3(N).

5
1
2
3
10
100

1
5
9
73
2302