A258979 - OEIS

%I #20 Sep 08 2022 08:46:13

%S 1,4,6,9,11,12,14,15,23,27,29,32,43,54,56,61,64,67,73,87,95,106,109,

%T 128,134,138,146,154,163,165,171,172,197,213,235,252,253,258,259,273,

%U 274,290,300,301,303,307,314,326,330,335,358,387,393,394,403,404,412

%N Numbers n such that 1 + sigma(n) + sigma(n)^2 + sigma(n)^3 + sigma(n)^4 is prime.

%H Robert Price, <a href="/A258979/b258979.txt">Table of n, a(n) for n = 1..932</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): A258979:=n->`if`(isprime(1 + sigma(n) + sigma(n)^2 + sigma(n)^3 + sigma(n)^4), n, NULL): seq(A258979(n), n=1..1000); # _Wesley Ivan Hurt_, Jul 09 2015

%t Select[ Range[10000], PrimeQ[ 1 + DivisorSigma[1, #] + DivisorSigma[1, #]^2 + DivisorSigma[1, #]^3 + DivisorSigma[1, #]^4] & ]

%t Select[ Range[10000], PrimeQ[ Cyclotomic[5, DivisorSigma[1, #]]] &]

%t Select[Range[10000],PrimeQ[Total[DivisorSigma[1,#]^Range[0,4]]]&] (* _Harvey P. Dale_, Aug 17 2015 *)

%o (Magma) [n: n in [1..500] | IsPrime(1 + DivisorSigma(1, n) + DivisorSigma(1, n)^2 + DivisorSigma(1, n)^3 + DivisorSigma(1, n)^4)]; // _Vincenzo Librandi_, Jun 16 2015

%o (PARI) is(n)=my(s=sigma(n)); isprime(s^4+s^3+s^2+s+1) \\ _Charles R Greathouse IV_, May 22 2017

%Y Cf. A000203, A258978, A258980.

%K nonn

%O 1,2

%A _Robert Price_, Jun 15 2015