|
Search: id:A062692
|
|
|
| A062692 |
|
Number of irreducible polynomials over F_2 of degree at most n. |
|
+0
4
|
|
| 2, 3, 5, 8, 14, 23, 41, 71, 127, 226, 412, 747, 1377, 2538, 4720, 8800, 16510, 31042, 58636, 111013, 210871, 401428, 766150, 1465020, 2807196, 5387991, 10358999, 19945394, 38458184, 74248451, 143522117, 277737797, 538038783, 1043325198
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
REFERENCES
|
Hicks, Kenneth H.; Mullen, Gary L.; and Sato, Ikuro, Distribution of irreducible polynomials over F_2, in Finite Fields with Applications to Coding Theory, Cryptography and Related Areas (Oaxaca, 2001), 177-186, Springer, Berlin, 2002.
|
|
FORMULA
|
Sum_{m=1..n} 1/m sum_{d | m } mu(d)*2^{m/d}.
|
|
MAPLE
|
with(numtheory):for n from 1 to 113 do sum3 := 0:for m from 1 to n do sum2 := 0:a := divisors(m):for h from 1 to nops(a) do sum2 := sum2+mobius(a[h])*2^(m/a[h]):end do:sum3 := sum3+sum2/m:end do:s[n] := sum3:end do:q := seq(s[j], j=1..113);
|
|
CROSSREFS
|
Partial sums of A001037.
a(n) = A091226(2^(n+1)). Cf. A014580, A091231.
Equals A001036 + 1.
Sequence in context: A000621 A039828 A005627 this_sequence A018154 A127603 A108351
Adjacent sequences: A062689 A062690 A062691 this_sequence A062693 A062694 A062695
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Gary L Mullen (mullen(AT)math.psu.edu), Jul 04 2001
|
|
EXTENSIONS
|
More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Mar 25 2002
|
|
|
Search completed in 0.002 seconds
|
