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

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

Author

Robert Price, Jun 20 2015

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000203, A259184, A259186.

Programs

Magma

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

Maple

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

Mathematica

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

PARI

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