login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A007839 Number of polynomials of degree n over GF(2) in which the degrees of all irreducible factors are distinct. 1
1, 2, 1, 4, 7, 14, 28, 54, 111, 218, 436, 854, 1735, 3432, 6825, 13664, 27352, 54218, 108714, 216616, 432239, 864548, 1727408, 3441364, 6891458, 13756440, 27466896, 54922134, 109751871, 219035562, 438319568, 875529382 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

A. Knopfmacher and R. Warlimont, Distinct degree factorizations for polynomials over a finite field, Trans. Amer. Math. Soc. 347 (1995), no. 6, 2235-2243.

FORMULA

G.f.: Product_{m>=1} (1 + pi(m) x^m), where pi(m) = A001037(m) = number of distinct irreducible polynomials of degree m.

EXAMPLE

a(3)=4 from x^3+x+1, x^3+x^2+1, x(x^2+x+1), (x+1)(x^2+x+1).

MATHEMATICA

max = 31; pi[n_] := Total[ MoebiusMu[n/#] * (2^#/n)& /@ Divisors[n]]; f[x_] := Product[ 1+pi[n]*x^n, {n, 1, max}]; CoefficientList[ Series[ f[x], {x, 0, max}], x] (* Jean-Fran├žois Alcover, Nov 24 2011 *)

CROSSREFS

Sequence in context: A139769 A326894 A275778 * A184345 A045625 A294501

Adjacent sequences:  A007836 A007837 A007838 * A007840 A007841 A007842

KEYWORD

nonn,easy,nice

AUTHOR

Arnold Knopfmacher

EXTENSIONS

More terms from David W. Wilson.

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 30 06:59 EDT 2020. Contains 333119 sequences. (Running on oeis4.)