log2(n+2) |
log2(n+1) |
∴a1•a2•a3…ak=
log23 |
log22 |
log24 |
log23 |
log2(k+2) |
log2(k+1) |
又∵a1•a2•a3…ak为整数
∴k+2必须是2的n次幂(n∈N*),即k=2n-2.
∴k∈[1,2009]内所有的企盼数的和M=(22-2)+(23-2)+(24-2)+…+(210-2)=
4(1−29) |
1−2 |
故答案为:2026.
log2(n+2) |
log2(n+1) |
log23 |
log22 |
log24 |
log23 |
log2(k+2) |
log2(k+1) |
4(1−29) |
1−2 |