A259308 -id:A259308 - cp's OEIS frontend

A259309 Numbers k such that 1 + sigma(k)^4 is prime.

1, 3, 5, 12, 14, 15, 19, 23, 28, 33, 34, 35, 39, 40, 47, 53, 57, 58, 73, 76, 79, 86, 88, 89, 104, 112, 116, 118, 126, 131, 133, 134, 138, 139, 145, 147, 148, 154, 163, 165, 173, 175, 179, 183, 185, 189, 193, 197, 201, 204, 206, 207, 213, 216, 219, 220, 224

Offset: 1

Robert Price, Jun 24 2015

Robert Price, Table of n, a(n) for n = 1..1459
OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

Cf. A000203, A259308, A259310.

[n: n in [1..250] | IsPrime(1+SumOfDivisors(n)^4)]; // Vincenzo Librandi, Jun 24 2015

with(numtheory): A259309:=n->`if`(isprime(1 + sigma(n)^4), n, NULL): seq(A259309(n), n=1..500); # Wesley Ivan Hurt, Jul 09 2015

Select[ Range[10000], PrimeQ[ 1 + DivisorSigma[1, #]^4] & ]
Select[ Range[10000], PrimeQ[ Cyclotomic[8, DivisorSigma[1, #]]] &]

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

A259310 Primes of the form: 1 + sigma(n)^4.

Original entry on oeis.org

2, 257, 1297, 614657, 331777, 331777, 160001, 331777, 9834497, 5308417, 8503057, 5308417, 9834497, 65610001, 5308417, 8503057, 40960001, 65610001, 29986577, 384160001, 40960001, 303595777, 1049760001, 65610001, 1944810001, 3782742017, 1944810001, 1049760001

Offset: 1

Robert Price, Jun 24 2015

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

Robert Price, Table of n, a(n) for n = 1..1459
OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

Cf. A000203, A259308, A259309.

[a: n in [1..150] | IsPrime(a) where a is 1 + SumOfDivisors(n)^4]; // Vincenzo Librandi, Jun 24 2015

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

Select[Table[1 + DivisorSigma[1, n]^4, {n, 10000}], PrimeQ]
Select[Table[Cyclotomic[8, DivisorSigma[1, n]], {n, 10000}], PrimeQ]

a(n) = A259308(A259309(n)).

cp's OEIS Frontend

A259309 Numbers k such that 1 + sigma(k)^4 is prime.

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