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A159908
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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.
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3
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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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.
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FORMULA
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PROG
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(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 ))
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CROSSREFS
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KEYWORD
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hard,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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