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

3, 2667, 3937, 57337, 172011, 253921, 677207307, 1073602561, 732959441001382539, 750688035198863979, 1000923107604038521, 1108158528150703969

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

Links

Table of n, a(n) for n=1..12.

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

Cf. A000203, A023194, A063103, A000668, A046528, A051027, A247821, A247822, A247954.

Sequence in context: A171361 A203687 A034316 * A003534 A202520 A281928

Adjacent sequences: A247835 A247836 A247837 * A247839 A247840 A247841

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