A259310 -id:A259310 - cp's OEIS frontend

A259308 a(n) = 1 + sigma(n)^4.

2, 82, 257, 2402, 1297, 20737, 4097, 50626, 28562, 104977, 20737, 614657, 38417, 331777, 331777, 923522, 104977, 2313442, 160001, 3111697, 1048577, 1679617, 331777, 12960001, 923522, 3111697, 2560001, 9834497, 810001, 26873857, 1048577, 15752962, 5308417

Offset: 1

Robert Price, Jun 24 2015

Robert Price, Table of n, a(n) for n = 1..10000
OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

Cf. A000203 (sum of divisors of n).

Cf. A259309 (indices of primes in this sequence), A259310 (corresponding primes).

[(1 + SumOfDivisors(n)^4): n in [1..50]]; // Vincenzo Librandi, Jun 24 2015

with(numtheory): A259308:=n->1+sigma(n)^4: seq(A259308(n), n=1..50); # Wesley Ivan Hurt, Jul 09 2015

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

a(n) = 1 + A000203(n)^4.

a(n) = A019326(A000203(n)). - Michel Marcus, Jun 24 2015

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

Original entry on oeis.org

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

cp's OEIS Frontend

A259308 a(n) = 1 + sigma(n)^4.

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