A292447 Primes p such that sigma((p + 1) / 2) is a prime q.

3, 7, 17, 31, 127, 577, 3361, 4801, 6961, 8191, 31249, 131071, 171697, 524287, 982801, 1062881, 1104097, 1367857, 1407841, 1468897, 2705137, 3770257, 6822817, 7785457, 10941841, 14183137, 15557041, 18495361, 20749681, 25304497, 36278161, 38878561, 44575681

Offset: 1

Author

Jaroslav Krizek, Sep 16 2017

Keywords

• nonn
• easy

Comments

A companion sequence of A249902.

Mersenne primes p = 2^k - 1 (A000668) are terms: sigma((p + 1) / 2) = sigma((2^k - 1 + 1) / 2) = sigma(2^(k - 1)) = 2^k - 1.

A subsequence of A178490. - Altug Alkan, Oct 02 2017

Examples

			17 is a term because sigma((17 + 1) / 2) = sigma(9) = 13 (prime).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A000668, A178490, A249902, A292448.

Programs

Magma

[n: n in [1..10^8] | IsPrime(n) and IsPrime(SumOfDivisors((n+1) div 2))];

Mathematica

Select[Prime@ Range[10^6], PrimeQ@ DivisorSigma[1, (# + 1)/2] &] (* Michael De Vlieger, Sep 16 2017 *)

PARI

lista(nn) = forprime(p=3, nn, if(isprime(sigma((p+1)/2)), print1(p, ", "))); \\ Altug Alkan, Oct 02 2017

Formula

a(n) = 2*A249902(n) - 1. - Altug Alkan, Oct 02 2017