OFFSET
1,1
COMMENTS
Subsequence of {A023194(n)+1}.
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.
Primes p such that A051027(p-1) = sigma(sigma(p-1)) = 2*(p-1). Subsequence of A256438. - Jaroslav Krizek, Mar 29 2015
From Jaroslav Krizek, Mar 17 2016: (Start)
From Jaroslav Krizek, Nov 27 2016: (Start)
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)
EXAMPLE
Prime 17 is in the sequence because sigma(17-1) = sigma(16) = 31 (prime).
MAPLE
with(numtheory): A249759:=n->`if`(isprime(n) and isprime(sigma(n-1)), n, NULL): seq(A249759(n), n=1..6*10^5); # Wesley Ivan Hurt, Nov 14 2014
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jaroslav Krizek, Nov 13 2014
STATUS
approved