These are the numbers with f factors which are also multiples of f.
1) 1: has one factor, 1.
2) 2: has two factors, 1 and 2.
3) 9: has three factors, 1, 3 and 9.
4) 8: has four factors, 1, 2, 4 and 8.
5) 625: has five factors, 1, 5, 25, 125 and 625.
6) 12: has six factors, 1, 2, 3, 4, 6 and 12
18: has six factors, 1, 2, 3, 6, 9 and 18.
7) 117649: has seven factors, 1, 7, 49, 343, 2401, 16807 and 117649
8) any odd prime (p) multiplied by 8 has eight factors, 1, 2, 4, 8, p, 2p, 4p and 8p.
Likewise 128: 1, 2, 4, 8, 16, 32, 64, 128.
9) the square of any prime (q) other than 3, multiplied by 9, has nine factors: 1, 3, 9, q, 3q, 9q, q2, 3q2 and 9q2
Likewise 6561: 1, 3, 9, 27, 81, 243, 729, 2187, 6561.
10) the only two numbers which have 10 factors and are themselves multiples of 10 are 80 and 1250.
80: 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80
1250: 1, 2, 5, 10, 25, 50, 125, 250, 625 and 1250.
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