A259251 -id:A259251 - cp's OEIS frontend

A259252 Numbers n such that 1 + sigma(n) + sigma(n)^2 + sigma(n)^3 + sigma(n)^4 + sigma(n)^5 + sigma(n)^6 is prime.

1, 2, 5, 9, 13, 16, 24, 25, 27, 28, 30, 37, 38, 39, 46, 50, 51, 55, 57, 59, 67, 68, 71, 79, 80, 82, 88, 93, 99, 105, 108, 118, 122, 125, 127, 133, 141, 145, 148, 152, 155, 157, 161, 162, 164, 179, 189, 191, 194, 196, 215, 228, 232, 237, 242, 247, 263, 281

Offset: 1

Robert Price, Jun 22 2015

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

Cf. A000203, A259251, A259253.

[n: n in [1..500] | IsPrime(1 + DivisorSigma(1, n) + DivisorSigma(1, n)^2 + DivisorSigma(1, n)^3 + DivisorSigma(1, n)^4 + DivisorSigma(1, n)^5+ DivisorSigma(1, n)^6)]; // Vincenzo Librandi, Jun 24 2015

with(numtheory): A259252:=n->`if`(isprime(1 + sigma(n) + sigma(n)^2 + sigma(n)^3 + sigma(n)^4 + sigma(n)^5 + sigma(n)^6), n, NULL): seq(A259252(n), n=1..500); # Wesley Ivan Hurt, Jul 09 2015

Select[Range[10000], PrimeQ[ 1 + DivisorSigma[1, #] + DivisorSigma[1, #]^2 + DivisorSigma[1, #]^3 + DivisorSigma[1, #]^4 + DivisorSigma[1, #]^5 + DivisorSigma[1, #]^6] &]
Select[Range[10000], PrimeQ[ Cyclotomic[7, DivisorSigma[1, #]]] &]

isok(n) = isprime(polcyclo(7, sigma(n))); \\ Michel Marcus, Jun 23 2015

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

Original entry on oeis.org

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

Offset: 1

Robert Price, Jun 22 2015

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

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

Cf. A000203, A259251, A259252.

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

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 *)

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

cp's OEIS Frontend

A259252 Numbers n such that 1 + sigma(n) + sigma(n)^2 + sigma(n)^3 + sigma(n)^4 + sigma(n)^5 + sigma(n)^6 is prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI