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 |