A Specific Case

$\text {Since } 27 = 3^3 \text { , therefore exactly those integers will be}$

$\text {coprime to 27, which are not divisible by 3. }$

Hence, we can get our sum S by applying PIE (the principle of inclusion-exclusion) and the sum of the arithmetic sequence formula:

$S = \frac { 27×(1+27) }{ 2 } - 3 × \frac { 9×(1+9) }{ 2 } = \boxed { 243 }$

Remark:

For the sake of simplicity, we summed the integers till 27 (despite the question says < 27), but we filtered the 27 out (since it is not coprime to itself), so we got the correct result in the end.