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%I #11 Sep 08 2022 08:46:13
%S 11,19,41,71,239,181,811,599,599,991,1559,419,599,3659,991,3191,929,
%T 2351,2969,2351,1481,3659,3191,9311,1979,2351,8741,2969,14519,14519,
%U 3659,9311,20879,4691,16001,9311,20879,38219,13109,19739,9311,34781,16001,14519,32579
%N Primes of the form sigma(n) + sigma(n)^2 - 1.
%C These primes are not sorted nor unique. They are listed in the order found.
%H K. D. Bajpai, <a href="/A259190/b259190.txt">Table of n, a(n) for n = 1..10000</a>
%e a(2) = 19: sigma(3) + sigma(3)^2 - 1 = 4 + 16 - 1 = 19, which is prime.
%e a(5) = 239: sigma(8) + sigma(8)^2 - 1 = 15 + 225 - 1 = 239, which is prime.
%p with(numtheory): A259190:= n-> (sigma(n) + sigma(n)^2-1): select(isprime,[seq((A259190 (n), n=1..500))]);
%t Select[Table[DivisorSigma[1, n] + DivisorSigma[1, n]^2 - 1, {n, 1, 10000}], PrimeQ]
%o (PARI) for(n=1, 100, k=sigma(n)+sigma (n)^2-1; if(isprime(k), print1(k,", "))); \\ _K. D. Bajpai_, Jun 20 2015
%o (Magma) [k: n in [1..100] | IsPrime(k) where k is SumOfDivisors(n)+ SumOfDivisors(n)^2-1]; // _K. D. Bajpai_, Jun 20 2015
%Y Cf. A000040, A000203, A258776.
%K nonn
%O 1,1
%A _K. D. Bajpai_, Jun 20 2015
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