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Primes of the form: 1 + sigma(n)^4.
3

%I #14 Sep 08 2022 08:46:13

%S 2,257,1297,614657,331777,331777,160001,331777,9834497,5308417,

%T 8503057,5308417,9834497,65610001,5308417,8503057,40960001,65610001,

%U 29986577,384160001,40960001,303595777,1049760001,65610001,1944810001,3782742017,1944810001,1049760001

%N Primes of the form: 1 + sigma(n)^4.

%C These primes are neither sorted nor uniqued. They are listed in the order found in A259308.

%H Robert Price, <a href="/A259310/b259310.txt">Table of n, a(n) for n = 1..1459</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) = A259308(A259309(n)).

%p with(numtheory): A259310:=n->`if`(isprime(1+sigma(n)^4), 1+sigma(n)^4, NULL): seq(A259310(n), n=1..200); # _Wesley Ivan Hurt_, Jul 09 2015

%t Select[Table[1 + DivisorSigma[1, n]^4, {n, 10000}], PrimeQ]

%t Select[Table[Cyclotomic[8, DivisorSigma[1, n]], {n, 10000}], PrimeQ]

%o (Magma) [a: n in [1..150] | IsPrime(a) where a is 1 + SumOfDivisors(n)^4]; // _Vincenzo Librandi_, Jun 24 2015

%Y Cf. A000203, A259308, A259309.

%K easy,nonn

%O 1,1

%A _Robert Price_, Jun 24 2015