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

1,1

Links

Robert Price, Table of n, a(n) for n = 1..10000

OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

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

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 *)

Prog

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

Crossrefs

Cf. A000203 (sum of divisors of n).

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

Sequence in context: A097993 A172806 A054752 * A128275 A028448 A108791

Adjacent sequences: A258975 A258976 A258977 * A258979 A258980 A258981

Keyword

easy,nonn

Author

Robert Price, Jun 15 2015

Status

approved