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

1,1

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 + A000203(n)^5 + A000203(n)^6.

a(n) = A053716(A000203(n)). - Michel Marcus, Jun 23 2015

Maple

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

Mathematica

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 *)

Prog

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

Crossrefs

Cf. A000203 (sum of divisors of n).

Cf. A259252 (indices of primes in this sequence), A259253 (corresponding primes).

Sequence in context: A139781 A101072 A203583 * A259253 A203871 A373037

Adjacent sequences: A259248 A259249 A259250 * A259252 A259253 A259254

Keyword

easy,nonn

Author

Robert Price, Jun 22 2015

Status

approved