Special modules

[sweety439]

* All quadratic residues are squares: {1, 2, 3, 4, 5, 8, 12, 16} (A254328)
* All quadratic residues are prime powers (including 1): {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 14, 16, 20, 32} (A254329)
* All quadratic residues are composites (including 1): {1, 2, 3, 4, 5, 8, 12, 15, 16, 24, 28, 40, 48, 56, 60, 72, 88, 112, 120, 168, 232, 240, 280, 312, 408, 520, 760, 840, 1320, 1848} (A065428)
* All coprime quadratic residues are squares: {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 21, 24, 28, 40, 48, 56, 60, 72, 88, 120, 168, 240, 840} (A303704)
* All coprime quadratic residues are prime powers (including 1): {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 24, 26, 28, 30, 32, 33, 35, 36, 40, 42, 44, 48, 51, 52, 54, 56, 60, 66, 72, 80, 84, 88, 90, 96, 104, 120, 132, 140, 144, 152, 168, 176, 180, 210, 240, 264, 300, 336, 360, 420, 480, 504, 840, 1680} (sequence is not in OEIS, the same sequence excluding the "1" is also not in OEIS)
* The only coprime quadratic residue is 1: {1, 2, 3, 4, 6, 8, 12, 24} (A018253)
* All coprime numbers are primes (including 1): {1, 2, 3, 4, 6, 8, 12, 18, 24, 30} (A048597)
* All coprime numbers are prime powers (including 1): {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 18, 20, 24, 30, 42, 60} (A051250)
* Odd modules such that all odd coprime numbers are primes (including 1): {1, 3, 5, 7, 9, 15, 21, 45, 105} (A327823)
* Odd modules such that all odd coprime numbers are prime powers (including 1): {1, 3, 5, 7, 9, 11, 13, 15, 21, 27, 33, 45, 75, 105} (sequence is not in OEIS)
* All coprime numbers in range (n,2*n) are primes (including 1): {1, 2, 4, 6, 10, 12} (sequence is not in OEIS, but see http://oeis.org/wiki/User:FUNG_Cheok...oof(i)_A048597)
* All coprime numbers in range (n,2*n) are prime powers (including 1): {1, 2, 3, 4, 6, 10, 12, 30} (sequence is not in OEIS)

Prove or disprove: All of these sets are complete.