1 2
1 3
1 4
2 3
2 4
3 4

==> gcd(ps, T) = ?; (1<=ps<q)
gsum(T) := 
1, 2 3 = 1+1
1, 2, 3, 4, 5 6 = 1+2+3+2+1=9
1, 2, 3, 4, 5, 6 7 = 1+1+1+1+1+1=6
1, 2, 3, 4, 5, 6, 7 8 = 1+2+1+4+1+2+1=12
1, 2, 3, 4, 5, 6, 7, 8 9 = 1+1+3+1+1+3+1+1
1...9 10 = 1+2+1+2+5+2+1+2+1
1...17 18 = 1+2+3+2+1+6+1+2+9+2+1+6+1+2+3+2+1
1...19 20 = 1+2+1+4+5+2+1+4+1+10+1+4+1+2+5+4+1+2+1

define fsum(T)=gsum(T)+T
fsum(2)=3
fsum(3)=5
fsum(4)=8
fsum(5)=9
fsum(6)=15
fsum(8)=20
fsum(10)=27
fsum(20)=72
==>fsum(p^e)=p^e+(p-1)p^(e-1)+p(p-1)p^(e-2)+p^2(p-1)p^(e-3)