A259369 -id:A259369 - cp's OEIS frontend

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

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

A259371 Primes of the form 1 + sigma(n)^3 + sigma(n)^6.

Original entry on oeis.org

3, 757, 262657, 64008001, 46656216001, 30841155073, 729027001, 46656216001, 30841155073, 225200075257, 885843322057, 46656216001, 41407378175593, 885843322057, 25002115044733, 1126163480473, 85766130261001, 191102989824001, 85766130261001, 41407378175593

Offset: 1

Robert Price, Jun 25 2015

These primes are neither sorted nor uniqued. They are listed in the order found in A259369.

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, A259370.

[a: n in [1..150] | IsPrime(a) where a is 1 + SumOfDivisors(n)^3 + SumOfDivisors(n)^6]; // Vincenzo Librandi, Jun 26 2015

with(numtheory): b:=n->1+sigma(n)^3+sigma(n)^6: A259371:=n->`if`( isprime(b(n)), b(n), NULL): seq(A259371(n), n=1..200); # Wesley Ivan Hurt, Jun 29 2015

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

a(n) = A259369(A259370(n)).

cp's OEIS Frontend

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

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