设{an}是集合{3^p+3^q+3^r I 0

0 ≤ p < q < r ,且 p ,q ,r ∈ N
an = 3^p + 3^q + 3^r
= 3^p [ 1 + 3^(q - p) + 3^(r - p) ]
ak = (3^4) · 31
3^1 = 3
3² = 9
3^3 = 27
∴p = 4 ,q - p = 1 ,r - p = 3
∴q = 5 ,r = 7
(p,q,r) = (4,5,7)
(4,5,7)
(3,5,7) (3,4,7)
(2,5,7) (2,4,7) (2,3,7)
(1,5,7) (1,4,7) (1,3,7) (1,2,7)
(0,5,7) (0,4,7) (0,3,7) (0,2,7) (0,1,7)
(4,5,6)
(3,5,6) (3,4,6)
(2,5,6) (2,4,6) (2,3,6)
(1,5,6) (1,4,6) (1,3,6) (1,2,6)
(0,5,6) (0,4,6) (0,3,6) (0,2,6) (0,1,6)
(3,4,5)
(2,4,5) (2,3,5)
(1,4,5) (1,3,5) (1,2,5)
(0,4,5) (0,3,5) (0,2,5) (0,1,5)
(2,3,4)
(1,3,4) (1,2,4)
(0,3,4) (0,2,4) (0,1,4)
(1,2,3)
(0,2,3) (0,1,3)
(0,1,2)
∴(5+4+3+2+1)×2+(4+3+2+1)+(3+2+1)+(2+1)+1=50

K等于50