A051664 -id:A051664 - cp's OEIS frontend

A086794 Numbers k such that the k-th cyclotomic polynomial has exactly 9 nonzero terms.

21, 42, 63, 84, 126, 147, 168, 189, 252, 294, 336, 378, 441, 504, 567, 588, 672, 756, 882, 1008, 1029, 1134, 1176, 1323, 1344, 1512, 1701, 1764, 2016, 2058, 2268, 2352, 2646, 2688, 3024, 3087, 3402, 3528, 3969, 4032, 4116, 4536, 4704, 5103, 5292

Offset: 1

Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 05 2003

nonn

Cf. A086779.

{k : A051664(k) = 9}. - R. J. Mathar, Sep 15 2012

A131456 Number of q-partial fraction summands of the reciprocal of n-th cyclotomic polynomial.

Original entry on oeis.org

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

Offset: 1

Augustine O. Munagi, Jul 12 2007

nonn

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)A000010).

			(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).

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

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

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A086794 Numbers k such that the k-th cyclotomic polynomial has exactly 9 nonzero terms.

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A131456 Number of q-partial fraction summands of the reciprocal of n-th cyclotomic polynomial.

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