A259184 -id:A259184 - cp's OEIS frontend

A259186 Primes in A259184.

7, 13, 43, 31, 211, 157, 307, 757, 307, 1483, 1723, 3541, 1723, 5113, 3907, 8191, 3541, 8011, 1723, 6007, 5113, 5113, 14281, 5113, 14281, 8011, 3541, 28057, 20593, 20593, 5113, 37831, 28057, 17293, 14281, 8011, 12433, 28057, 20593, 14281, 24181, 10303, 46441

Offset: 1

Robert Price, Jun 20 2015

These primes are neither sorted nor uniqued. They are listed in the order found in A259184.

Robert Price, Table of n, a(n) for n = 1..1737
OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

Cf. A000203, A259184, A259185.

with(numtheory): A259186:=n->`if`(isprime(1 - sigma(n) + sigma(n)^2), 1 - sigma(n) + sigma(n)^2, NULL): seq(A259186(n), n=1..200); # Wesley Ivan Hurt, Jul 09 2015

Select[Table[1 - DivisorSigma[1, n] + DivisorSigma[1, n]^2, {n, 10000}], PrimeQ]
Select[Table[Cyclotomic[6, DivisorSigma[1, n]], {n, 10000}], PrimeQ]

a(n) = A259184(A259185(n)).

A259185 Numbers n such that 1 - sigma(n) + sigma(n)^2 is prime.

Original entry on oeis.org

2, 3, 4, 5, 8, 9, 10, 12, 17, 18, 20, 24, 26, 30, 32, 36, 38, 40, 41, 45, 46, 51, 54, 55, 56, 58, 59, 60, 66, 70, 71, 72, 78, 86, 87, 89, 91, 92, 94, 95, 99, 101, 102, 104, 106, 108, 110, 115, 116, 119, 123, 125, 131, 134, 138, 142, 143, 144, 154, 159, 164

Offset: 1

Robert Price, Jun 20 2015

Robert Price, Table of n, a(n) for n = 1..1737
OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

Cf. A000203, A259184, A259186.

[n: n in [1..180] | IsPrime(1 - SumOfDivisors(n) + SumOfDivisors(n)^2)]; // Vincenzo Librandi, Nov 20 2015

with(numtheory): A259185:=n->`if`(isprime(1 - sigma(n) + sigma(n)^2), n, NULL): seq(A259185(n), n=1..500); # Wesley Ivan Hurt, Jul 09 2015

Select[ Range[10000], PrimeQ[ 1 - DivisorSigma[1, n] + DivisorSigma[1, n]^2] & ]
Select[ Range[10000], PrimeQ[ Cyclotomic[6, DivisorSigma[1, #]]] &]

is(n)=my(s=sigma(n)); isprime(s^2-s+1) \\ Charles R Greathouse IV, May 22 2017

cp's OEIS Frontend

A259186 Primes in A259184.

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