|
| |
|
|
A086257
|
|
Number of primitive prime factors of 2^n+1.
|
|
4
| |
|
|
1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 3, 1, 1, 2, 2, 1, 2, 2, 3, 2, 2, 2, 3, 1, 1, 2, 2, 1, 2, 1, 4, 2, 2, 1, 3, 3, 2, 2, 2, 2, 2, 2, 2, 3, 1, 1, 4, 1, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 4, 1, 3, 3, 4, 1, 2, 3, 4, 5, 2, 1, 4, 1, 3, 3, 3, 3, 1, 2, 3, 2, 1, 4, 3, 2, 4, 1, 4, 2, 1
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,15
|
|
|
COMMENTS
| A prime factor of 2^n+1 is called primitive if it does not divide 2^r+1 for any r<n. Zsigmondy's theorem says that there is at least one primitive prime factor except for n=3. See A086258 for those n that have a record number of primitive prime factors.
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=0..500 (using data from A001269)
Eric Weisstein's World of Mathematics, Zsigmondy Theorem
|
|
|
EXAMPLE
| a(14) = 2 because 2^14+1 = 5*29*113 and 29 and 113 do not divide 2^r+1 for r < 14.
|
|
|
MATHEMATICA
| nMax=200; pLst={}; Table[f=Transpose[FactorInteger[2^n+1]][[1]]; f=Complement[f, pLst]; cnt=Length[f]; pLst=Union[pLst, f]; cnt, {n, 0, nMax}]
|
|
|
CROSSREFS
| Cf. A046799 (number of distinct prime factors of 2^n+1), A054992 (number of prime factors, with repetition, of 2^n+1), A086258.
Sequence in context: A050330 A205788 A076398 * A161098 A136177 A066922
Adjacent sequences: A086254 A086255 A086256 * A086258 A086259 A086260
|
|
|
KEYWORD
| hard,nonn
|
|
|
AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Jul 14 2003
|
| |
|
|
