cp's OEIS Frontend

A292446 Numbers k such that sigma((k + 1) / 2) is a prime q.

%I A292446 #40 Nov 24 2024 01:49:50
%S A292446 3,7,17,31,49,127,577,1457,3361,4801,6961,8191,10081,15841,20401,
%T A292446 31249,34321,55777,57121,59857,131071,167041,171697,293377,524287,
%U A292446 559681,916657,982801,1062881,1104097,1158241,1195057,1367857,1407841,1414561,1468897,1659841
%N A292446 Numbers k such that sigma((k + 1) / 2) is a prime q.
%C A292446 Corresponding values of primes q are in A062700.
%C A292446 Prime terms are in A292447.
%C A292446 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 A292446 This sequence also has terms of the form p^(q-1) where p and q are odd primes, i.e., A002315(1)^2 = 7^2 and A002315(3)^2 = 239^2. Terms that are not squarefree are 49, 55777, 57121, 167041, 2789521, 50060017, ... - _Altug Alkan_, Oct 02 2017
%H A292446 Amiram Eldar, <a href="/A292446/b292446.txt">Table of n, a(n) for n = 1..10000</a>
%F A292446 a(n) = 2*A023194(n) - 1.
%e A292446 49 is a term because sigma((49 + 1) / 2) = sigma(25) = 31 (prime).
%t A292446 Select[Range[1,166*10^4,2],PrimeQ[DivisorSigma[1,(#+1)/2]]&] (* _Harvey P. Dale_, Jun 22 2022 *)
%o A292446 (Magma) [n: n in [1..10^8] | IsOdd(n) and IsPrime(SumOfDivisors((n+1) div 2))];
%o A292446 (PARI) isok(n) = (n%2) && isprime(sigma((n+1)/2)); \\ _Michel Marcus_, Sep 16 2017
%Y A292446 Cf. A000203, A000668, A023194, A023195, A062700, A292447, A292448.
%K A292446 nonn,easy
%O A292446 1,1
%A A292446 _Jaroslav Krizek_, Sep 16 2017