login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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

%I #21 Sep 08 2022 08:46:13

%S 7,1093,5461,137257,55987,3257437,299593,12204241,5229043,36012943,

%T 3257437,499738093,8108731,199411801,199411801,917087137,36012943,

%U 3611342281,67368421,5622910567,1108378657,2238976117,199411801,47446779661,917087137,5622910567

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

%H Robert Price, <a href="/A259251/b259251.txt">Table of n, a(n) for n = 1..10000</a>

%H OEIS Wiki, <a href="https://oeis.org/wiki/Cyclotomic Polynomials at x=n, n! and sigma(n)">Cyclotomic Polynomials at x=n, n! and sigma(n)</a>

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

%F a(n) = A053716(A000203(n)). - _Michel Marcus_, Jun 23 2015

%p 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

%t 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}]

%t Table[Cyclotomic[7, DivisorSigma[1, n]], {n, 10000}]

%t f[n_] := Total[DivisorSigma[1, n]^Range[0, 6]]; Array[f, 26] (* _Robert G. Wilson v_ *)

%o (PARI) vector(30, n, polcyclo(7, sigma(n))) \\ _Michel Marcus_, Jun 23 2015

%o (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

%Y Cf. A000203 (sum of divisors of n).

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

%K easy,nonn

%O 1,1

%A _Robert Price_, Jun 22 2015