As stated, the first such pair is 80 and 81:

80 = 2*2*2*2*5

81 = 3*3*3*3

Others follow below, with the numbers followed by their counts of unique primes and all primes including duplicates:

80 2      5

81 1      4

135 2      4

136 2      4

224 2      6

225 2      4

296 2      4

297 2      4

350 3      4

351 2      4

351 2      4

352 2      6

375 2      4

376 2      4

440 3      5

441 2      4

If however we want to count only unique (that is, different) primes, the first pair is 7314 and 7315:

7314 = 2*3*23*53

7315 = 5*7*11*19

others follow:

7314 4      4

7315 4      4

8294 4      4

8295 4      4

8645 4      4

8646 4      4

9009 4      5

9010 4      4