

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
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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(n1). 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(n1) + 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



