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A057719
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Prime factors of numbers in A006521 (numbers k that divide 2^k + 1).
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6
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3, 19, 163, 571, 1459, 8803, 9137, 17497, 41113, 52489, 78787, 87211, 135433, 139483, 144667, 164617, 174763, 196579, 274081, 370009, 370387, 478243, 760267, 941489, 944803, 1041619, 1220347, 1236787, 1319323, 1465129, 1663579, 1994659
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OFFSET
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1,1
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COMMENTS
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A prime p is in this sequence iff all prime divisors of ord_p(2)/2 are in this sequence, where ord_p(2) is the order of 2 modulo p. - Max Alekseyev, Jul 30 2006
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LINKS
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Alexander Kalmynin, On Novák numbers, arXiv:1611.00417 [math.NT], 2016. See Chapter 4 p. 7 Novák primes.
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EXAMPLE
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2^171 + 1 == 0 (mod 171), 171 = 3^2*19, 2^13203+1 == 0 (mod 13203), 13203 = 3^4*163.
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MATHEMATICA
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S = {2}; Reap[For[p = 3, p < 2 10^6, p = NextPrime[p], f = FactorInteger[ MultiplicativeOrder[2, p]]; If[f[[1, 1]] != 2 || f[[1, 2]] != 1, Continue[]]; f = f[[All, 1]]; If[Length[Intersection[S, f]] == Length[f], S = Union[S, {p}]; Print[p]; Sow[p]]]][[2, 1]] (* Jean-François Alcover, Nov 11 2018, from PARI *)
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PROG
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(PARI) { A057719() = local(S, f); S=Set([2]); forprime(p=3, 10^7, f=factorint(znorder(Mod(2, p))); if(f[1, 1]!=2||f[1, 2]!=1, next); f=f[, 1]; if(length(setintersect(S, Set(f)))==length(f), S=setunion(S, [p]); print1(p, ", "))) }
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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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