A259252 -id:A259252 - cp's OEIS frontend

A259251 a(n) = 1 + sigma(n) + sigma(n)^2 + sigma(n)^3 + sigma(n)^4 + sigma(n)^5 + sigma(n)^6.

7, 1093, 5461, 137257, 55987, 3257437, 299593, 12204241, 5229043, 36012943, 3257437, 499738093, 8108731, 199411801, 199411801, 917087137, 36012943, 3611342281, 67368421, 5622910567, 1108378657, 2238976117, 199411801, 47446779661, 917087137, 5622910567

Offset: 1

Robert Price, Jun 22 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. A259252 (indices of primes in this sequence), A259253 (corresponding primes).

[1 + SumOfDivisors(n) + SumOfDivisors(n)^2 + SumOfDivisors(n)^3 + SumOfDivisors(n)^4 + SumOfDivisors(n)^5 + SumOfDivisors(n)^6: n in [1..50]]; // Vincenzo Librandi, Jun 26 2015

with(numtheory): A259251:=n->1 + sigma(n) + sigma(n)^2 + sigma(n)^3 + sigma(n)^4 + sigma(n)^5 + sigma(n)^6: seq(A259251(n), n=1..50); # Wesley Ivan Hurt, Jul 09 2015

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}]
Table[Cyclotomic[7, DivisorSigma[1, n]], {n, 10000}]
f[n_] := Total[DivisorSigma[1, n]^Range[0, 6]]; Array[f, 26] (* Robert G. Wilson v *)

vector(30, n, polcyclo(7, sigma(n))) \\ Michel Marcus, Jun 23 2015

a(n) = 1 + A000203(n) + A000203(n)^2 + A000203(n)^3 + A000203(n)^4 + A000203(n)^5 + A000203(n)^6.

a(n) = A053716(A000203(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

A259251 a(n) = 1 + sigma(n) + sigma(n)^2 + sigma(n)^3 + sigma(n)^4 + sigma(n)^5 + sigma(n)^6.

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