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A247838 Numbers k such that sigma(sigma(k)) is prime.

%I A247838 #49 Jul 10 2025 19:39:39
%S A247838 3,2667,3937,57337,172011,253921,677207307,1073602561,
%T A247838 732959441001382539,750688035198863979,1000923107604038521,
%U A247838 1108158528150703969
%N A247838 Numbers k such that sigma(sigma(k)) is prime.
%C A247838 Numbers k such that A051027(k) is a prime p.
%C A247838 Prime 3 is the only prime p such that sigma(sigma(p)) is a prime q.
%C A247838 Conjecture: Subsequence of A046528 (numbers that are a product of distinct Mersenne primes).
%C A247838 Corresponding values of primes p: 7, 8191, 8191, 131071, 524287, 524287, ... (A247822). Conjecture: values of primes p is equal to Mersenne primes (A000668).
%C A247838 732959441001382539, 750688035198863979, 1000923107604038521, 1108158528150703969 and 196751176038481899983340171 are terms. - _Jaroslav Krizek_, Mar 25 2015
%C A247838 a(9) > 10^10. - _Michel Marcus_, Feb 13 2020
%C A247838 a(13) > 10^19. - _Giovanni Resta_, Feb 14 2020
%F A247838 a(n) = 2*A247821(n)-1.
%e A247838 2667 is a term because sigma(sigma(2667)) = sigma(4096) = 8191 (i.e., prime).
%p A247838 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 A247838 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 A247838 (Magma) [n: n in [1..10000000] | IsPrime(SumOfDivisors(SumOfDivisors(n)))];
%o A247838 (PARI) isok(n) = isprime(sigma(sigma(n))); \\ _Michel Marcus_, Oct 01 2014
%Y A247838 Cf. A000203, A023194, A063103, A000668, A046528, A051027, A247821, A247822, A247954.
%K A247838 nonn,more
%O A247838 1,1
%A A247838 _Jaroslav Krizek_, Sep 28 2014
%E A247838 a(7)-a(8) from _Michel Marcus_, Oct 02 2014
%E A247838 a(9)-a(12) from _Giovanni Resta_, Feb 14 2020