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A091248 Number of irreducible factors in the factorization of X^n + 1 over GF(2) (counted with multiplicity). 3
1, 2, 2, 4, 2, 4, 3, 8, 3, 4, 2, 8, 2, 6, 5, 16, 3, 6, 2, 8, 6, 4, 3, 16, 3, 4, 4, 12, 2, 10, 7, 32, 5, 6, 6, 12, 2, 4, 5, 16, 3, 12, 4, 8, 8, 6, 3, 32, 5, 6, 8, 8, 2, 8, 5, 24, 5, 4, 2, 20, 2, 14, 13, 64, 7, 10, 2, 12, 6, 12, 3, 24, 9, 4, 8, 8, 6, 10, 3, 32, 5, 6, 2, 24, 12, 8, 5, 16, 9, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

A. Karttunen, Scheme-program for computing this sequence.

Index entries for sequences operating on GF(2)[X]-polynomials

FORMULA

a(n) = A091222(A000051(n)).

a(n) = Sum_{d|n} A318622(d). - Robert Israel, Aug 30 2018

MAPLE

h:= proc(n) option remember;  numtheory:-phi(n)/numtheory:-order(2, n/2^padic:-ordp(n, 2)) end proc:

f:= n -> add(h(d), d=numtheory:-divisors(n)):

map(f, [$1..100]); # Robert Israel, Aug 30 2018

CROSSREFS

Cf. A000374 gives the number of distinct irreducible factors of the same polynomials.

Sequence in context: A182730 A214560 A152858 * A082991 A214212 A100008

Adjacent sequences:  A091245 A091246 A091247 * A091249 A091250 A091251

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jan 03 2004

STATUS

approved

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Last modified October 23 09:28 EDT 2019. Contains 328345 sequences. (Running on oeis4.)