A259410 -id:A259410 - cp's OEIS frontend

A259411 Numbers n such that 1 - sigma(n) + sigma(n)^2 - sigma(n)^3 + sigma(n)^4 is prime.

2, 6, 11, 19, 33, 35, 37, 47, 57, 68, 79, 81, 82, 88, 118, 121, 129, 145, 157, 162, 179, 217, 226, 241, 245, 257, 258, 260, 262, 289, 306, 332, 378, 393, 430, 434, 441, 461, 465, 466, 473, 474, 477, 483, 485, 490, 499, 504, 509, 512, 518, 526, 528, 533, 550

Offset: 1

Robert Price, Jun 26 2015

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

Cf. A000203, A259410, A259412.

[n: n in [1..600] | IsPrime(1 - DivisorSigma(1, n) + DivisorSigma(1, n)^2 - DivisorSigma(1, n)^3 + DivisorSigma(1, n)^4)]; // Vincenzo Librandi, Jun 27 2015

with(numtheory): A259411:=n->`if`(isprime(1-sigma(n)+sigma(n)^2-sigma(n)^3+sigma(n)^4), n, NULL): seq(A259411(n), n=1..1000); # Wesley Ivan Hurt, Jul 09 2015

Select[ Range[10000], PrimeQ[ 1 - DivisorSigma[1, #] + DivisorSigma[1, #]^2 - DivisorSigma[1, #]^3 + DivisorSigma[1, #]^4] & ]
Select[ Range[10000], PrimeQ[ Cyclotomic[10, DivisorSigma[1, #]]] &]

is(n)=my(s=sigma(n)); isprime(s^4-s^3+s^2-s+1) \\ Charles R Greathouse IV, May 22 2017

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

Original entry on oeis.org

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

Robert Price, Jun 26 2015

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

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

Cf. A000203, A259410, A259411.

[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

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

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 *)

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

cp's OEIS Frontend

A259411 Numbers n such that 1 - sigma(n) + sigma(n)^2 - sigma(n)^3 + sigma(n)^4 is prime.

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