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

2, 4, 16, 65536

Offset: 1

Author

Jaroslav Krizek, Nov 13 2014

Keywords

• nonn
• more

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

Examples

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

Crossrefs

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

Programs

Magma

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

Mathematica

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

Formula

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