cp's OEIS Frontend

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

%I A292447 #31 Nov 23 2024 19:37:38
%S A292447 3,7,17,31,127,577,3361,4801,6961,8191,31249,131071,171697,524287,
%T A292447 982801,1062881,1104097,1367857,1407841,1468897,2705137,3770257,
%U A292447 6822817,7785457,10941841,14183137,15557041,18495361,20749681,25304497,36278161,38878561,44575681
%N A292447 Primes p such that sigma((p + 1) / 2) is a prime q.
%C A292447 A companion sequence of A249902.
%C A292447 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.
%C A292447 A subsequence of A178490. - _Altug Alkan_, Oct 02 2017
%H A292447 Amiram Eldar, <a href="/A292447/b292447.txt">Table of n, a(n) for n = 1..10000</a>
%F A292447 a(n) = 2*A249902(n) - 1. - _Altug Alkan_, Oct 02 2017
%e A292447 17 is a term because sigma((17 + 1) / 2) = sigma(9) = 13 (prime).
%t A292447 Select[Prime@ Range[10^6], PrimeQ@ DivisorSigma[1, (# + 1)/2] &] (* _Michael De Vlieger_, Sep 16 2017 *)
%o A292447 (Magma) [n: n in [1..10^8] | IsPrime(n) and IsPrime(SumOfDivisors((n+1) div 2))];
%o A292447 (PARI) lista(nn) = forprime(p=3, nn, if(isprime(sigma((p+1)/2)), print1(p, ", "))); \\ _Altug Alkan_, Oct 02 2017
%Y A292447 Cf. A000203, A000668, A178490, A249902, A292448.
%K A292447 nonn,easy
%O A292447 1,1
%A A292447 _Jaroslav Krizek_, Sep 16 2017