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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
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 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, "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: A078559 A317557 A338763 * 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 October 4 06:54 EDT 2022. Contains 357237 sequences. (Running on oeis4.)