A259371 -id:A259371 - cp's OEIS frontend

A259369 a(n) = 1 + sigma(n)^3 + sigma(n)^6.

3, 757, 4161, 117993, 46873, 2987713, 262657, 11394001, 4829007, 34018057, 2987713, 481912257, 7532281, 191116801, 191116801, 887533473, 34018057, 3518803081, 64008001, 5489105833, 1073774593, 2176828993, 191116801, 46656216001, 887533473, 5489105833

Offset: 1

Robert Price, Jun 25 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), A060883 (n^6 + n^3 + 1).

Cf. A259370 (indices of primes in this sequence), A259371 (corresponding primes).

[1+SumOfDivisors(n)^3+ SumOfDivisors(n)^6: n in [1..50]]; // Vincenzo Librandi, Jun 26 2015

with(numtheory): A259369:=n->1+sigma(n)^3+sigma(n)^6: seq(A259369(n), n=1..40); # Wesley Ivan Hurt, Jun 29 2015

Table[1 + DivisorSigma[1, n]^3 + DivisorSigma[1, n]^6, {n, 10000}]
Table[Cyclotomic[9, DivisorSigma[1, n]], {n, 10000}]

a(n) = polcyclo(9, sigma(n)) \\ Michel Marcus, Jun 25 2015

a(n) = 1 + A000203(n)^3 + A000203(n)^6.

a(n) = A060883(A000203(n)). - Michel Marcus, Jun 25 2015

A259370 Numbers n such that 1 + sigma(n)^3 + sigma(n)^6 is prime.

Original entry on oeis.org

1, 2, 7, 19, 24, 28, 29, 38, 39, 45, 52, 59, 80, 97, 98, 101, 104, 114, 116, 122, 135, 146, 152, 158, 162, 177, 196, 197, 199, 203, 204, 209, 211, 220, 224, 232, 239, 242, 246, 261, 277, 284, 286, 290, 296, 298, 334, 358, 365, 389, 397, 415, 443, 444, 445

Offset: 1

Robert Price, Jun 25 2015

Robert Price, Table of n, a(n) for n = 1..756
OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

Cf. A000203, A259369, A259371.

[n: n in [1..500] | IsPrime(1 + DivisorSigma(1, n)^3 + DivisorSigma(1, n)^6)]; // Vincenzo Librandi, Jun 27 2015

with(numtheory): A259370:=n->`if`(isprime(1+sigma(n)^3+sigma(n)^6), n, NULL): seq(A259370(n), n=1..1000); # Wesley Ivan Hurt, Jul 09 2015

Select[ Range[10000], PrimeQ[ 1 + DivisorSigma[1, #]^3 + DivisorSigma[1, #]^6] & ]
Select[ Range[10000], PrimeQ[ Cyclotomic[9, DivisorSigma[1, #]]] &]
Select[Range[500],PrimeQ[Total[DivisorSigma[1,#]^{0,3,6}]]&] (* Harvey P. Dale, May 29 2023 *)

is(n)=my(s=sigma(n)); isprime(s^6+s^3+1) \\ Charles R Greathouse IV, May 22 2017

cp's OEIS Frontend

A259369 a(n) = 1 + sigma(n)^3 + sigma(n)^6.

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