Primitive Prime Factor

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

REFERENCES:

Sloane, N. J. A. Sequence A005529/M1505 in "The On-Line Encyclopedia of Integer Sequences."