|
|
A249903
|
|
Numbers n such that 2n+1 and sigma(n) are both noncomposite numbers.
|
|
1
|
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
If a(5) exists, it must be a square bigger than 3*10^8.
Conjecture: 2 and 9 are the only numbers n such that 2n - 1, 2n + 1 and sigma(n) are all primes.
a(n) (n >= 3) must be of the form 3^(2k) for some positive integer k.
(End)
|
|
LINKS
|
|
|
EXAMPLE
|
Number 729 is in the sequence because 2*729 + 1 = 1459 and sigma(729) = 1093 (both primes).
|
|
MATHEMATICA
|
Join[{1}, Select[Range[0, 1000], PrimeQ[DivisorSigma[1, #]]&& PrimeQ[2 # + 1] &]] (* Vincenzo Librandi, Nov 14 2014 *)
Join[{1}, Select[Range[1000], AllTrue[{2#+1, DivisorSigma[1, #]}, PrimeQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 06 2019 *)
|
|
PROG
|
(Magma) [1] cat [n: n in [1..10000000] | IsPrime(2*n+1) and IsPrime(SumOfDivisors(n))]; // corrected by Vincenzo Librandi, Nov 14 2014
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|