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A249759
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Primes p such that sigma(p-1) is a prime q.
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13
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OFFSET
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1,1
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COMMENTS
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Conjectures: 1) sequence is finite; 2) sequence is a subsequence of A019434 (Fermat primes); 3) sequence consists of Fermat primes p such that sigma(p-1) is a Mersenne prime; 4) a(n) = (A249761(n)+3)/2.
3 is the only prime p such that sigma(p+1) is prime, i.e., 3 is the only prime p such that sigma(p-1) and sigma(p+1) are both primes.
Conjecture: 3 is the only number n such that n and sigma(n+1) are both prime.
Corresponding values of primes q are in A249761: 3, 7, 31, 131071, ...
Conjecture: also primes p such that tau(p-1) is a prime q; corresponding values of primes q are 2, 3, 5, 17. (End)
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LINKS
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FORMULA
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EXAMPLE
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Prime 17 is in the sequence because sigma(17-1) = sigma(16) = 31 (prime).
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MAPLE
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MATHEMATICA
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Select[Range[10^5], PrimeQ[#]&& PrimeQ[DivisorSigma[1, # - 1]] &] (* Vincenzo Librandi, Nov 14 2014 *)
Select[Prime[Range[7000]], PrimeQ[DivisorSigma[1, #-1]]&] (* Harvey P. Dale, Jun 14 2020 *)
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PROG
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(Magma) [p: p in PrimesUpTo(1000000) | IsPrime(SumOfDivisors(p-1))]
(PARI) lista(nn) = {forprime(p=1, nn, if (isprime(sigma(p-1)), print1(p, ", ")); ); } \\ Michel Marcus, Nov 14 2014
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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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STATUS
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approved
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