login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A086798 Number of coefficients equal to zero in n-th cyclotomic polynomial. 2
0, 0, 0, 1, 0, 0, 0, 3, 4, 0, 0, 2, 0, 0, 2, 7, 0, 4, 0, 4, 4, 0, 0, 6, 16, 0, 16, 6, 0, 2, 0, 15, 6, 0, 8, 10, 0, 0, 8, 12, 0, 4, 0, 10, 18, 0, 0, 14, 36, 16, 10, 12, 0, 16, 24, 18, 12, 0, 0, 10, 0, 0, 28, 31, 18, 6, 0, 16, 14, 8, 0, 22, 0, 0, 34, 18, 30, 8, 0, 28, 52, 0, 0, 16, 24, 0, 18, 30, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,8
REFERENCES
See A051664.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537 (terms 1..1000 from T. D. Noe)
FORMULA
From Benoit Cloitre, Aug 06 2003: (Start)
a(4n+2) = a(2n+1); a(4n) = a(2n) + phi(2n).
When p is an odd prime and m integer >= 1: a(p^m) = a(2*p^m) = p^m - p^(m-1) - p + 1. In particular a(p) = a(2p) = 0. (End)
a(n) = 1 + phi(n) - A051664(n). - T. D. Noe, Aug 08 2003
MATHEMATICA
Table[Count[CoefficientList[Cyclotomic[n, x], x], _?(#==0&)], {n, 0, 100}]
PROG
(PARI) a(n)=sum(k=0, eulerphi(n), if(polcoeff(polcyclo(n), k), 0, 1))
(PARI) A086798(n) = (1 + eulerphi(n) - length(select(x->x!=0, Vec(polcyclo(n))))); \\ Antti Karttunen, Sep 21 2018
CROSSREFS
Cf. A051664 (number of nonzero terms in n-th cyclotomic polynomial).
Sequence in context: A025096 A261137 A319341 * A155061 A322016 A247446
KEYWORD
nonn
AUTHOR
Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 05 2003
EXTENSIONS
More terms from Benoit Cloitre and T. D. Noe, Aug 06 2003
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)