A258978 a(n) = 1 + sigma(n) + sigma(n)^2 + sigma(n)^3 + sigma(n)^4.

5, 121, 341, 2801, 1555, 22621, 4681, 54241, 30941, 111151, 22621, 637421, 41371, 346201, 346201, 954305, 111151, 2374321, 168421, 3187591, 1082401, 1727605, 346201, 13179661, 954305, 3187591, 2625641, 10013305, 837931, 27252361, 1082401, 16007041, 5421361

Offset: 1

Author

Robert Price, Jun 15 2015

Keywords

• easy
• nonn

Links

• Robert Price, Table of n, a(n) for n = 1..10000
• OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

Crossrefs

Cf. A000203 (sum of divisors of n).

Cf. A258979 (indices of primes in this sequence), A258980 (corresponding primes).

Programs

Magma

[(1 + DivisorSigma(1, n) + DivisorSigma(1, n)^2 + DivisorSigma(1, n)^3 + DivisorSigma(1, n)^4): n in [1..35]]; // Vincenzo Librandi, Jun 16 2015

Maple

with(numtheory): A258978:=n->1+sigma(n)+sigma(n)^2+sigma(n)^3+sigma(n)^4: seq(A258978(n), n=1..40); # Wesley Ivan Hurt, Jul 09 2015

Mathematica

Table[1 + DivisorSigma[1, n] + DivisorSigma[1, n]^2 + DivisorSigma[1, n]^3 + DivisorSigma[1, n]^4, {n, 10000}]
Table[Cyclotomic[5, DivisorSigma[1, n]], {n, 10000}]
Total/@Table[DivisorSigma[1,n]^ex,{n,40},{ex,0,4}] (* Harvey P. Dale, Jun 24 2017 *)

PARI

vector(50, n, polcyclo(6, sigma(n))) \\ Michel Marcus, Jun 25 2015

Formula

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

a(n) = A053699(A000203(n)). - Michel Marcus, Jun 25 2015