|
| |
|
|
A046800
|
|
Number of distinct prime factors of 2^n-1.
|
|
9
| |
|
|
0, 0, 1, 1, 2, 1, 2, 1, 3, 2, 3, 2, 4, 1, 3, 3, 4, 1, 4, 1, 5, 3, 4, 2, 6, 3, 3, 3, 6, 3, 6, 1, 5, 4, 3, 4, 8, 2, 3, 4, 7, 2, 6, 3, 7, 6, 4, 3, 9, 2, 7, 5, 7, 3, 6, 6, 8, 4, 6, 2, 11, 1, 3, 6, 7, 3, 8, 2, 7, 4, 9, 3, 12, 3, 5, 7, 7, 4, 7, 3, 9, 6, 5, 2, 12, 3, 5, 6, 10, 1, 11, 5, 9, 3, 6, 5, 12, 2, 5, 8, 12, 2
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,5
|
|
|
COMMENTS
| Length of row n of A060443.
|
|
|
REFERENCES
| J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=0..500 (derived from Brillhart et al.)
J. Brillhart et al., Factorizations of b^n +- 1 Available on-line
|
|
|
FORMULA
| a[ n ] = Length[ FactorInteger [ 2^n -1 ] ]
a(n) = Sum{d|n} A086251(d), Mobius transform of A086251.
|
|
|
EXAMPLE
| a[6] = 2 because 63 = 3*3*7 has 2 distinct prime factors
|
|
|
MATHEMATICA
| Table[Length[ FactorInteger [ 2^n -1 ] ], {n, 0, 100}]
|
|
|
CROSSREFS
| Cf. A000225.
Cf. A046051 (number of prime factors, with repetition, of 2^n-1), A086251.
Sequence in context: A143773 A191372 A053279 * A027350 A029327 A079135
Adjacent sequences: A046797 A046798 A046799 * A046801 A046802 A046803
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
|
|
|
EXTENSIONS
| Edited by T. D. Noe (noe(AT)sspectra.com), Jul 14 2003
|
| |
|
|
