OFFSET
1,1
COMMENTS
Numbers n such that A051027(n) is a prime p.
Prime 3 is the only prime p such that sigma(sigma(p)) is a prime q.
Conjecture: Subsequence of A046528 (numbers that are a product of distinct Mersenne primes).
Corresponding values of primes p: 7, 8191, 8191, 131071, 524287, 524287, ... (A247822). Conjecture: values of primes p is equal to Mersenne primes (A000668).
732959441001382539, 750688035198863979, 1000923107604038521, 1108158528150703969 and 196751176038481899983340171 are terms. - Jaroslav Krizek, Mar 25 2015
a(9) > 10^10. - Michel Marcus, Feb 13 2020
a(13) > 10^19. - Giovanni Resta, Feb 14 2020
FORMULA
a(n) = 2*A247821(n)-1.
EXAMPLE
2667 is a term because sigma(sigma(2667)) = sigma(4096) = 8191 (i.e., prime).
MAPLE
with(numtheory): A247838:=n->`if`(isprime(sigma(sigma(n))), n, NULL): seq(A247838(n), n=1..10^5); # Wesley Ivan Hurt, Oct 02 2014
MATHEMATICA
Select[Range[260000], PrimeQ[DivisorSigma[1, DivisorSigma[1, #]]]&] (* The program generates the first six terms of the sequence. *) (* Harvey P. Dale, Jan 18 2024 *)
PROG
(Magma) [n: n in [1..10000000] | IsPrime(SumOfDivisors(SumOfDivisors(n)))]
(PARI) isok(n) = isprime(sigma(sigma(n))); \\ Michel Marcus, Oct 01 2014
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jaroslav Krizek, Sep 28 2014
EXTENSIONS
a(7)-a(8) from Michel Marcus, Oct 02 2014
a(9)-a(12) from Giovanni Resta, Feb 14 2020
STATUS
approved