A249760 Numbers k such that k+1 and sigma(kn) are both primes.

2, 4, 16, 65536

Offset

1,1

Comments

4 is the only number k such that k-1 and sigma(k) are both primes.

Corresponding values of k+1 and sigma(k) are in A249759 and A249761.

Conjectures: (1) sequence is finite; (2) a(n) + 1 is a Fermat prime (A019434); (3) sigma(a(n)) is a Mersenne prime (A000668).

Subsequence of A023194, and by a comment in that entry it follows that each term is a prime power. From that conjectures (2) and (3) above easily follow. - Jeppe Stig Nielsen, Jan 13 2015

Links

Table of n, a(n) for n=1..4.

Formula

a(n) = A249759(n) - 1.

Example

16 is a term because 16+1=17 and sigma(16)=31 are both primes.

Mathematica

Select[Range[10^5], PrimeQ[# + 1]&& PrimeQ[DivisorSigma[1, #]] &] (* Vincenzo Librandi, Nov 14 2014 *)

Prog

(Magma) [n: n in [1..10^8] | IsPrime(n+1) and IsPrime(SumOfDivisors(n))]

Crossrefs

Cf. A000203, A000668, A019434, A249759, A249761.

Sequence in context: A124436 A369378 A014221 * A271552 A105510 A155951

Adjacent sequences: A249757 A249758 A249759 * A249761 A249762 A249763

Keyword

nonn,more

Author

Jaroslav Krizek, Nov 13 2014

Status

approved