A259253 Primes of the form: 1 + sigma(n) + sigma(n)^2 + sigma(n)^3 + sigma(n)^4 + sigma(n)^5 + sigma(n)^6.

7, 1093, 55987, 5229043, 8108731, 917087137, 47446779661, 917087137, 4201025641, 31401724537, 141276239497, 3092313043, 47446779661, 31401724537, 141276239497, 654022685443, 141276239497, 141276239497, 265462278481, 47446779661, 100343116693, 4033516174507

Offset: 1

Author

Robert Price, Jun 22 2015

Keywords

• easy
• nonn

Comments

These primes are neither sorted nor uniqued. They are listed in the order found in A259251.

Links

• Robert Price, Table of n, a(n) for n = 1..885
• OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

Crossrefs

Cf. A000203, A259251, A259252.

Programs

Maple

with(numtheory): A259253:=n->`if`(isprime(1 + sigma(n) + sigma(n)^2 + sigma(n)^3 + sigma(n)^4+sigma(n)^5+sigma(n)^6), 1 + sigma(n) + sigma(n)^2 + sigma(n)^3 + sigma(n)^4 + sigma(n)^5 + sigma(n)^6, NULL): seq(A259253(n), n=1..100); # Wesley Ivan Hurt, Jul 09 2015

Mathematica

Select[Table[1 + DivisorSigma[1, n] + DivisorSigma[1, n]^2 + DivisorSigma[1, n]^3 + DivisorSigma[1, n]^4 + DivisorSigma[1, n]^5 + DivisorSigma[1, n]^6, {n, 10000}], PrimeQ]
Select[Table[Cyclotomic[7, DivisorSigma[1, n]], {n, 10000}], PrimeQ]
Select[Table[Total[DivisorSigma[1,n]^Range[0,6]],{n,80}],PrimeQ] (* Harvey P. Dale, Oct 09 2020 *)

Formula

a(n) = A259251(A259252(n)).