Primitive Prime Factor
المؤلف:
Sloane, N. J. A.
المصدر:
Sequence A005529/M1505 in "The On-Line Encyclopedia of Integer Sequences."
الجزء والصفحة:
...
16-9-2020
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Primitive Prime Factor
Given an integer sequence ![<span style=]()
{a_n}_(n=1)^infty" src="https://mathworld.wolfram.com/images/equations/PrimitivePrimeFactor/Inline1.gif" style="height:17px; width:42px" />, 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 ![<span style=]()
{k^2+1}_(k=1)^(10)" src="https://mathworld.wolfram.com/images/equations/PrimitivePrimeFactor/Inline9.gif" style="height:22px; width:64px" /> 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."
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