%I #20 May 29 2023 11:21:35

%S 1,2,7,19,24,28,29,38,39,45,52,59,80,97,98,101,104,114,116,122,135,

%T 146,152,158,162,177,196,197,199,203,204,209,211,220,224,232,239,242,

%U 246,261,277,284,286,290,296,298,334,358,365,389,397,415,443,444,445

%N Numbers n such that 1 + sigma(n)^3 + sigma(n)^6 is prime.

%H Robert Price, <a href="/A259370/b259370.txt">Table of n, a(n) for n = 1..756</a>

%H OEIS Wiki, <a href="https://oeis.org/wiki/Cyclotomic Polynomials at x=n, n! and sigma(n)">Cyclotomic Polynomials at x=n, n! and sigma(n)</a>

%p with(numtheory): A259370:=n->`if`(isprime(1+sigma(n)^3+sigma(n)^6), n, NULL): seq(A259370(n), n=1..1000); # _Wesley Ivan Hurt_, Jul 09 2015

%t Select[ Range[10000], PrimeQ[ 1 + DivisorSigma[1, #]^3 + DivisorSigma[1, #]^6] & ]

%t Select[ Range[10000], PrimeQ[ Cyclotomic[9, DivisorSigma[1, #]]] &]

%t Select[Range[500],PrimeQ[Total[DivisorSigma[1,#]^{0,3,6}]]&] (* _Harvey P. Dale_, May 29 2023 *)

%o (Magma) [n: n in [1..500] | IsPrime(1 + DivisorSigma(1, n)^3 + DivisorSigma(1, n)^6)]; // _Vincenzo Librandi_, Jun 27 2015

%o (PARI) is(n)=my(s=sigma(n)); isprime(s^6+s^3+1) \\ _Charles R Greathouse IV_, May 22 2017

%Y Cf. A000203, A259369, A259371.

%K easy,nonn

%O 1,2

%A _Robert Price_, Jun 25 2015