login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A131456 Number of q-partial fraction summands of the reciprocal of n-th cyclotomic polynomial. 0
1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 8, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 7, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 10, 1, 2, 1, 2, 1, 2, 1, 2, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Let Phi(n,q) be the n-th cyclotomic polynomial in q. The q-partial fraction decomposition of 1/Phi(n,q) is a representation of 1/Phi(n,q) as a finite sum of functions v(q)/(1-q^m)^t, such that m<=n and degree(v)<phi(m) (Euler's totient function A000010).

LINKS

Table of n, a(n) for n=1..105.

Augustine O. Munagi, Computation of q-partial fractions, INTEGERS: Electronic Journal Of Combinatorial Number Theory, 7 (2007), #A25.

Eric Weisstein's World of Mathematics, Cyclotomic Polynomial

EXAMPLE

(i) a(3)=1 because 1/Phi(3,q)=(1-q)/(1-q^3);

(ii) a(6)=2 because 1/Phi(6,q)=(-1-q)/(1-q^3) + (2+2q)/(1-q^6).

CROSSREFS

Cf. A051664 (Number of terms in n-th cyclotomic polynomial).

Sequence in context: A161263 A161288 A185217 * A074944 A245041 A161315

Adjacent sequences:  A131453 A131454 A131455 * A131457 A131458 A131459

KEYWORD

nonn

AUTHOR

Augustine O. Munagi, Jul 12 2007

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 October 18 02:23 EDT 2019. Contains 328135 sequences. (Running on oeis4.)