Search: a070524 -id:a070524
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A070525
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Numbers n such that n-th cyclotomic polynomial evaluated at phi(n) is a prime number.
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+10
3
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2, 3, 4, 6, 7, 8, 12, 18, 21, 30, 45, 48, 70, 120, 127, 153, 182, 204, 212, 282, 318, 322, 910, 1167, 1177, 1342, 1680, 1963, 2670, 4398, 4655, 8088, 8599, 8808, 19680
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OFFSET
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1,1
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COMMENTS
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These are probable primes for n > 910. No others for n <= 10000. The prime values of n are 2, 3, 7, 127 and 8599 (A088856). - T. D. Noe, Nov 23 2003
All terms <= 2670, except 1963, have been certified prime with PARI's ECPP. There are no other terms <= 25000. - Lucas A. Brown, Jan 08 2021
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LINKS
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EXAMPLE
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n=7: Phi(7)=6, Cyclotomic(7,6)=1+6+36+216+1296+7776+46656=55987 is prime.
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MATHEMATICA
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Do[s=Cyclotomic[n, EulerPhi[n]]; If[PrimeQ[s], Print[n]], {n, 1, 400}]
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PROG
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(PARI) isok(n) = isprime(polcyclo(n, eulerphi(n))); \\ Michel Marcus, Sep 01 2019
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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