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Search: id:A159908
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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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+0
3
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| 1, 3, 6, 9, 13, 15, 19, 23, 27, 30, 34, 35, 43, 40
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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, "Cyclotomic polynomial puzzles", in: "primenumbers" group, May 9, 2009.
Eric W. Weisstein, "Cyclotomic Polynomial", in: MathWorld--A Wolfram Web Resource.
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FORMULA
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a(n) = A008486(n-1) + A159909(n)
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PROGRAM
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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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Sequence in context: A065811 A061514 A078559 this_sequence A088364 A022853 A059540
Adjacent sequences: A159905 A159906 A159907 this_sequence A159909 A159910 A159911
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KEYWORD
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hard,more,nonn
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AUTHOR
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M. F. Hasler (MHasler(AT)univ-ag.fr), May 09 2009
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