A249902 -id:A249902 - cp's OEIS frontend

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

Jaroslav Krizek, Sep 16 2017

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

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

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

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

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

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

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

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

A249903 Numbers n such that 2n+1 and sigma(n) are both noncomposite numbers.

Original entry on oeis.org

1, 2, 9, 729

Offset: 1

Jaroslav Krizek, Nov 14 2014

If a(5) exists, it must be a square bigger than 3*10^8.
Intersection of A005097 and A023194.
Conjecture: 2 and 9 are the only numbers n such that 2n - 1, 2n + 1 and sigma(n) are all primes.
From Hiroaki Yamanouchi, Nov 19 2014: (Start)
a(n) (n >= 3) must be of the form 3^(2k) for some positive integer k.
a(5) (if it exists) >= 3^877000 (see A003306 and A028491).
(End)

			Number 729 is in the sequence because 2*729 + 1 = 1459 and sigma(729) = 1093 (both primes).

Cf. A000203, A003306, A005097, A023194, A028491, A249902.

[1] cat [n: n in [1..10000000] | IsPrime(2*n+1) and IsPrime(SumOfDivisors(n))]; // corrected by Vincenzo Librandi, Nov 14 2014

Join[{1}, Select[Range[0, 1000], PrimeQ[DivisorSigma[1, #]]&& PrimeQ[2 # + 1] &]] (* Vincenzo Librandi, Nov 14 2014 *)
Join[{1},Select[Range[1000],AllTrue[{2#+1,DivisorSigma[1,#]},PrimeQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 06 2019 *)

cp's OEIS Frontend

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

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