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%I #24 Sep 08 2022 08:46:13
%S 61,19141,19141,152381,5200081,5200081,2031671,5200081,40454321,
%T 250062751,40454321,212601841,250062751,1043960221,1043960221,
%U 310565641,954091601,1043960221,619281791,17315368621,1043960221,4278255361,13640692231,3415627931,13640692231
%N Primes of the form 1 - sigma(n) + sigma(n)^2 - sigma(n)^3 + sigma(n)^4.
%C These primes are neither sorted nor uniqued. They are listed in the order found in A259410.
%H Robert Price, <a href="/A259412/b259412.txt">Table of n, a(n) for n = 1..1017</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>
%F a(n) = A259410(A259411(n)).
%p with(numtheory): A259412:=n->`if`(isprime(1-sigma(n)+sigma(n)^2-sigma(n)^3+sigma(n)^4), 1-sigma(n)+sigma(n)^2-sigma(n)^3+sigma(n)^4, NULL): seq(A259412(n), n=1..500); # _Wesley Ivan Hurt_, Jun 27 2015
%t Select[Table[1 - DivisorSigma[1, n] + DivisorSigma[1, n]^2 - DivisorSigma[1, n]^3 + DivisorSigma[1, n]^4, {n, 10000}], PrimeQ]
%t Select[Table[Cyclotomic[10, DivisorSigma[1, n]], {n, 10000}], PrimeQ]
%t Select[1-#+#^2-#^3+#^4&/@DivisorSigma[1,Range[300]],PrimeQ] (* _Harvey P. Dale_, Jul 07 2017 *)
%o (Magma) [a: n in [1..300] | IsPrime(a) where a is (1 - SumOfDivisors(n) + SumOfDivisors(n)^2 - SumOfDivisors(n)^3 + SumOfDivisors(n)^4)]; // _Vincenzo Librandi_, Jun 27 2015
%Y Cf. A000203, A259410, A259411.
%K easy,nonn
%O 1,1
%A _Robert Price_, Jun 26 2015
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