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%I #46 Jan 18 2024 18:33:58
%S 3,2667,3937,57337,172011,253921,677207307,1073602561,
%T 732959441001382539,750688035198863979,1000923107604038521,
%U 1108158528150703969
%N Numbers n such that sigma(sigma(n)) is prime.
%C Numbers n such that A051027(n) is a prime p.
%C Prime 3 is the only prime p such that sigma(sigma(p)) is a prime q.
%C Conjecture: Subsequence of A046528 (numbers that are a product of distinct Mersenne primes).
%C Corresponding values of primes p: 7, 8191, 8191, 131071, 524287, 524287, ... (A247822). Conjecture: values of primes p is equal to Mersenne primes (A000668).
%C 732959441001382539, 750688035198863979, 1000923107604038521, 1108158528150703969 and 196751176038481899983340171 are terms. - _Jaroslav Krizek_, Mar 25 2015
%C a(9) > 10^10. - _Michel Marcus_, Feb 13 2020
%C a(13) > 10^19. - _Giovanni Resta_, Feb 14 2020
%F a(n) = 2*A247821(n)-1.
%e 2667 is a term because sigma(sigma(2667)) = sigma(4096) = 8191 (i.e., prime).
%p with(numtheory): A247838:=n->`if`(isprime(sigma(sigma(n))),n,NULL): seq(A247838(n), n=1..10^5); # _Wesley Ivan Hurt_, Oct 02 2014
%t Select[Range[260000],PrimeQ[DivisorSigma[1,DivisorSigma[1,#]]]&] (* The program generates the first six terms of the sequence. *) (* _Harvey P. Dale_, Jan 18 2024 *)
%o (Magma) [n: n in [1..10000000] | IsPrime(SumOfDivisors(SumOfDivisors(n)))]
%o (PARI) isok(n) = isprime(sigma(sigma(n))); \\ _Michel Marcus_, Oct 01 2014
%Y Cf. A000203, A023194, A063103, A000668, A046528, A051027, A247821, A247822, A247954.
%K nonn,more
%O 1,1
%A _Jaroslav Krizek_, Sep 28 2014
%E a(7)-a(8) from _Michel Marcus_, Oct 02 2014
%E a(9)-a(12) from _Giovanni Resta_, Feb 14 2020
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