Given an integer sequence , a prime number is said to be a primitive prime factor of the term if divides but does not divide any for . It is possible for a term to have zero, one, or many primitive prime factors.
For example, the prime factors of the sequence are summarized in the following table (OEIS A005529).
prime factorization | prime factors | primitive prime factors | ||
1 | 2 | 2 | 2 | 2 |
2 | 5 | 5 | 5 | 5 |
3 | 10 | 2, 5 | ||
4 | 17 | 17 | 17 | 17 |
5 | 26 | 2, 13 | 13 | |
6 | 37 | 37 | 37 | 37 |
7 | 50 | 2, 5 | ||
8 | 65 | 5, 13 | ||
9 | 82 | 2, 41 | 41 | |
10 | 101 | 101 | 101 | 101 |