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.

%I A259251 #21 Sep 08 2022 08:46:13
%S A259251 7,1093,5461,137257,55987,3257437,299593,12204241,5229043,36012943,
%T A259251 3257437,499738093,8108731,199411801,199411801,917087137,36012943,
%U A259251 3611342281,67368421,5622910567,1108378657,2238976117,199411801,47446779661,917087137,5622910567
%N A259251 a(n) = 1 + sigma(n) + sigma(n)^2 + sigma(n)^3 + sigma(n)^4 + sigma(n)^5 + sigma(n)^6.
%H A259251 Robert Price, <a href="/A259251/b259251.txt">Table of n, a(n) for n = 1..10000</a>
%H A259251 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 A259251 a(n) = 1 + A000203(n) + A000203(n)^2 + A000203(n)^3 + A000203(n)^4 + A000203(n)^5 + A000203(n)^6.
%F A259251 a(n) = A053716(A000203(n)). - _Michel Marcus_, Jun 23 2015
%p A259251 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 A259251 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 A259251 Table[Cyclotomic[7, DivisorSigma[1, n]], {n, 10000}]
%t A259251 f[n_] := Total[DivisorSigma[1, n]^Range[0, 6]]; Array[f, 26] (* _Robert G. Wilson v_ *)
%o A259251 (PARI) vector(30, n, polcyclo(7, sigma(n))) \\ _Michel Marcus_, Jun 23 2015
%o A259251 (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 A259251 Cf. A000203 (sum of divisors of n).
%Y A259251 Cf. A259252 (indices of primes in this sequence), A259253 (corresponding primes).
%K A259251 easy,nonn
%O A259251 1,1
%A A259251 _Robert Price_, Jun 22 2015