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A159908 Number of pairs (p,q) of primes p <= q <= r=prime(n) such that the cyclotomic polynomial Phi(p*q*r) has no coefficient > 1 in absolute value. 3
1, 3, 6, 9, 13, 15, 19, 23, 27, 30, 34, 35, 43, 40 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The cyclotomic polynomial Phi[pqr] (p,q,r primes) can only have coefficients with absolute value > 1 if p,q,r are distinct odd primes. This sequence also counts the trivial cases where (1): p=2, or (2): p=q, or (3): q=r. The number of these cases is A008486(n-1). Sequence A159909 counts only the nontrivial cases.

LINKS

Table of n, a(n) for n=1..14.

Phil Carmody, "Cyclotomic polynomial puzzles", in: "primenumbers" group, May 9, 2009.

Phil Carmody, David Broadhurst, Maximilian Hasler, Makoto Kamada, Cyclotomic polynomial puzzles, digest of 43 messages in primenumbers Yahoo group, May 9, 2009 - May 23, 2013.

Eric W. Weisstein, "Cyclotomic Polynomial"

FORMULA

a(n) = A008486(n-1) + A159909(n)

PROG

(PARI) A159908(n) = sum( i=1, n, my(pq=prime(n)*prime(i)); sum( j=1, i, vecmax(abs(Vec(polcyclo(prime(j)*pq))))==1 ))

CROSSREFS

Sequence in context: A061514 A078559 A317557 * A236761 A088364 A022853

Adjacent sequences:  A159905 A159906 A159907 * A159909 A159910 A159911

KEYWORD

hard,more,nonn

AUTHOR

M. F. Hasler, May 09 2009

STATUS

approved

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)