A039776 Number of new fractions m/n, where m is 1 or composite, (m,n) = 1 and "new" means the value of mn has not occurred before.

1, 1, 1, 1, 2, 1, 3, 1, 3, 2, 6, 1, 7, 2, 4, 3, 10, 1, 11, 1, 5, 4, 14, 1, 12, 5, 10, 3, 19, 1, 20, 6, 9, 7, 13, 2, 25, 7, 10, 5, 28, 1, 29, 5, 8, 9, 32, 3, 28, 5, 14, 7, 37, 3, 18, 9, 16, 13, 42, 1, 43, 12, 15, 15, 21, 2, 48, 10, 20, 4, 51, 4, 52, 15, 12, 11, 30, 2, 57, 8, 33, 18, 60, 1