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A225185
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Primes p which do not have a primitive root that divides p+1.
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2
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7, 23, 31, 43, 47, 71, 73, 79, 103, 127, 151, 157, 167, 191, 193, 199, 223, 239, 241, 263, 271, 277, 283, 311, 313, 331, 337, 359, 367, 383, 397, 409, 431, 439, 457, 463, 479, 487, 503, 571, 577, 599, 607, 631, 647, 673, 691, 719, 727, 733, 739, 743, 751, 811, 823, 839, 863, 887, 911, 919, 967, 983, 991, 997
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OFFSET
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1,1
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LINKS
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EXAMPLE
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The primitive roots modulo 97 are 5, 7, 10, 13, 14, 15, 17, 21, 23, 26, 29, 37, 38, 39, ..., and 7 divides 98, so 97 is not a term of this sequence.
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MATHEMATICA
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q[n_] := PrimeQ[n] && AllTrue[PrimitiveRootList[n], ! Divisible[n + 1, #] &]; Select[Range[1000], q] (* Amiram Eldar, Oct 07 2021 *)
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PROG
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(PARI) forprime(p=2, 1000, i=0; fordiv(p+1, X, if(znorder(Mod(X, p))==eulerphi(p), i=1)); if(i==0, print1(p", "))) \\ V. Raman, May 04 2012
(Magma) [p: p in PrimesUpTo(1000) | not exists{r: r in [1..p-1] | IsPrimitive(r, p) and IsZero((p+1) mod r)}]; // Bruno Berselli, May 10 2013
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CROSSREFS
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KEYWORD
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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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