|
Search: id:A086257
|
|
|
| A086257 |
|
Number of primitive prime factors of 2^n+1. |
|
+0
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; listen)
|
|
|
OFFSET
|
0,15
|
|
|
COMMENT
|
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: A102097 A050330 A076398 this_sequence A161098 A136177 A066922
Adjacent sequences: A086254 A086255 A086256 this_sequence A086258 A086259 A086260
|
|
KEYWORD
|
hard,nonn
|
|
AUTHOR
|
T. D. Noe (noe(AT)sspectra.com), Jul 14 2003
|
|
|
Search completed in 0.002 seconds
|
