A259412 Primes of the form 1 - sigma(n) + sigma(n)^2 - sigma(n)^3 + sigma(n)^4.

61, 19141, 19141, 152381, 5200081, 5200081, 2031671, 5200081, 40454321, 250062751, 40454321, 212601841, 250062751, 1043960221, 1043960221, 310565641, 954091601, 1043960221, 619281791, 17315368621, 1043960221, 4278255361, 13640692231, 3415627931, 13640692231

Offset: 1

Author

Robert Price, Jun 26 2015

Keywords

• easy
• nonn

Comments

These primes are neither sorted nor uniqued. They are listed in the order found in A259410.

Links

• Robert Price, Table of n, a(n) for n = 1..1017
• OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

Crossrefs

Cf. A000203, A259410, A259411.

Programs

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

Maple

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

Mathematica

Select[Table[1 - DivisorSigma[1, n] + DivisorSigma[1, n]^2 - DivisorSigma[1, n]^3 + DivisorSigma[1, n]^4, {n, 10000}], PrimeQ]
Select[Table[Cyclotomic[10, DivisorSigma[1, n]], {n, 10000}], PrimeQ]
Select[1-#+#^2-#^3+#^4&/@DivisorSigma[1,Range[300]],PrimeQ] (* Harvey P. Dale, Jul 07 2017 *)

Formula

a(n) = A259410(A259411(n)).