A158526 -id:A158526 - cp's OEIS frontend

2, 3, 5, 11, 23, 59, 71, 113, 131, 137, 149, 179, 227, 257, 263, 269, 293, 317, 347, 353, 401, 419, 443, 449, 467, 557, 653, 659, 677, 683, 743, 773, 809, 839, 857, 881, 911, 929, 947, 977, 1019, 1049, 1277, 1301, 1319, 1433, 1571, 1697, 1847, 1871, 1901, 1913

Offset: 1

Jaroslav Krizek, Sep 01 2015

nonn

Primes p such that (number of divisors of p * sum of divisors of p * product of divisors of p - 1) is also a prime.
Primes p such that (A000005(p) * A000203(p) * A007955(p) - 1) is also a prime.
See similar sequences of type primes p such that x is also a prime for some x wherein tau(p) = A000005(p) = number of divisors of p, sigma(p) = A000203(p) = sum of divisors of p and pod(p) = A007955(p) = product of divisors of p:
A001359 (for x = tau(p) + sigma(p) - 1 and x = tau(p) + pod(p)),
A005382 (for x = tau(p) * pod(p) - 1),
A005384 (for x = sigma(p) + pod(p), x = tau(p) * sigma(p) - 1 and x = tau(p) * pod(p) + 1),
A023200 (for x = tau(p) + sigma(p) + 1),
A023204 (for x = tau(p) + sigma(p) + pod(p) and x = tau(p) * sigma(p) + 1),
A053182 (for x = sigma(p) * pod(p) + 1),
A053184 (for x = sigma(p) * pod(p) - 1),
A158526 (for x = tau(p) * sigma(p) * pod(p) + 1).
For n >= 3, a(n) == 5 mod 6. - Robert Israel, Sep 02 2015

			3 and 2*3^2 + 2*3 - 1 = 23 are primes.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000005, A000203, A007955.

Cf. A001359, A005382, A005384, A023200, A023204, A053182, A053184, A158526.

[n: n in[1..10000] | IsPrime(n) and IsPrime(2*n*n + 2*n - 1)];

select(t -> isprime(t) and isprime(2*t^2 + 2*t-1), [2,3,seq(6*i-1,i=1..1000)]); # Robert Israel, Sep 02 2015

Select[Prime[Range[300]], PrimeQ[2 #^2 + 2 # - 1] &] (* Vincenzo Librandi, Sep 02 2015 *)

is(n)=isprime(n)&&isprime(2*n^2 + 2*n - 1) \\ Anders Hellström, Sep 01 2015

cp's OEIS Frontend

A261810 n and (2n^2 + 2n - 1) are primes.

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