A258775 Numbers n such that 1 + sigma(n)+ sigma(n)^2 is prime.

1, 2, 5, 6, 7, 8, 11, 13, 14, 15, 19, 23, 34, 37, 40, 45, 49, 53, 57, 58, 60, 61, 78, 79, 89, 92, 105, 106, 109, 123, 129, 132, 137, 138, 140, 141, 143, 148, 149, 154, 155, 156, 160, 161, 163, 165, 167, 182, 188, 191, 193, 195, 201, 208, 212, 213, 222, 226

Offset: 1

Author

Robert Price, Jun 09 2015

Keywords

• nonn

Comments

Also numbers n such that A000203(n) is in A002384. - Robert Israel, Jun 09 2015

Links

• Robert Price, Table of n, a(n) for n = 1..2122
• OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

Crossrefs

Cf. A002384, A000203, A258774, A258776.

Programs

Magma

[n: n in [1..250] | IsPrime(1 + SumOfDivisors(n)+ SumOfDivisors(n)^2)]; // Vincenzo Librandi, Jun 10 2015

Maple

select(isprime @ (t -> 1+t+t^2) @ numtheory:-sigma, [$1..1000]); # Robert Israel, Jun 09 2015

Mathematica

Select[ Range[10000], PrimeQ[ 1 + DivisorSigma[1, #] + DivisorSigma[1, #]^2] & ]
Select[ Range[10000], PrimeQ[ Cyclotomic[3, DivisorSigma[1, #]]] &]

PARI

for(n=1,10^3,if(isprime(1+sigma(n)+sigma(n)^2),print1(n,", "))) \\ Derek Orr, Jun 09 2015