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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, 45, 47, 54, 57, 58, 64, 69, 69, 71, 79, 79, 84, 86, 87, 97, 96, 94, 107, 106, 109, 120, 111, 120, 123, 124, 133, 135, 134, 144, 143, 143, 154, 154, 154, 163, 161, 167, 175, 174, 175, 179, 183, 187, 191, 193, 199, 197, 202, 203 (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
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 Weisstein's World of Mathematics, 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: A078559 A317557 A338763 * A236761 A088364 A022853
KEYWORD
hard,nonn
AUTHOR
M. F. Hasler, May 09 2009
EXTENSIONS
More terms from Robin Visser, Aug 09 2023
STATUS
approved

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Last modified April 22 09:25 EDT 2024. Contains 371894 sequences. (Running on oeis4.)