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%I #19 Sep 08 2022 08:46:13
%S 1,2,5,9,13,16,24,25,27,28,30,37,38,39,46,50,51,55,57,59,67,68,71,79,
%T 80,82,88,93,99,105,108,118,122,125,127,133,141,145,148,152,155,157,
%U 161,162,164,179,189,191,194,196,215,228,232,237,242,247,263,281
%N Numbers n such that 1 + sigma(n) + sigma(n)^2 + sigma(n)^3 + sigma(n)^4 + sigma(n)^5 + sigma(n)^6 is prime.
%H Robert Price, <a href="/A259252/b259252.txt">Table of n, a(n) for n = 1..885</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>
%p with(numtheory): A259252:=n->`if`(isprime(1 + sigma(n) + sigma(n)^2 + sigma(n)^3 + sigma(n)^4 + sigma(n)^5 + sigma(n)^6), n, NULL): seq(A259252(n), n=1..500); # _Wesley Ivan Hurt_, Jul 09 2015
%t Select[Range[10000], PrimeQ[ 1 + DivisorSigma[1, #] + DivisorSigma[1, #]^2 + DivisorSigma[1, #]^3 + DivisorSigma[1, #]^4 + DivisorSigma[1, #]^5 + DivisorSigma[1, #]^6] &]
%t Select[Range[10000], PrimeQ[ Cyclotomic[7, DivisorSigma[1, #]]] &]
%o (PARI) isok(n) = isprime(polcyclo(7, sigma(n))); \\ _Michel Marcus_, Jun 23 2015
%o (Magma) [n: n in [1..500] | IsPrime(1 + DivisorSigma(1, n) + DivisorSigma(1, n)^2 + DivisorSigma(1, n)^3 + DivisorSigma(1, n)^4 + DivisorSigma(1, n)^5+ DivisorSigma(1, n)^6)]; // _Vincenzo Librandi_, Jun 24 2015
%Y Cf. A000203, A259251, A259253.
%K easy,nonn
%O 1,2
%A _Robert Price_, Jun 22 2015
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