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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. A086765, A086780.

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

Sequence in context: A025096 A261137 A319341 * A155061 A322016 A247446

Adjacent sequences:  A086795 A086796 A086797 * A086799 A086800 A086801

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

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Last modified August 18 14:22 EDT 2022. Contains 356215 sequences. (Running on oeis4.)