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A063783 Sum of cube of divisors is prime. 4

%I

%S 4,9,121,36481,72361,146689,259081,654481,683929,786769,1985281,

%T 2036329,3193369,3636649,3798601,4583881,5031049,5470921,5555449,

%U 6135529,6713281,7284601,7778521

%N Sum of cube of divisors is prime.

%H Harry J. Smith, <a href="/A063783/b063783.txt">Table of n, a(n) for n=1..1000</a>

%F Solutions to DivisorSigma[3, x]=prime.

%e All these terms are squares of primes (2, 3, 11, 191, 269, 383, 509, 809, 827, 887, 1409, 1427, 1787, 1907, 1949, 2141, 2243, 2339, 2357, 2477, 2591, 2699, 2789), so their DivisorSigma[3, p^2] = p^6+p^3+1 has polynomial of degree 6.

%e sigma[3,9]=1+27+729=757, a prime.

%t Select[Prime[Range[500]]^2, PrimeQ@ DivisorSigma[3, #] &] (* _Michael De Vlieger_, Jul 16 2017 *)

%o (PARI) { n=0; p=0; for (m=1, 10^9, p=nextprime(p+1); if(isprime(p^6 + p^3 + 1), write("b063783.txt", n++, " ", p^2); if (n==1000, break)) ) } \\ _Harry J. Smith_, Aug 31 2009

%Y Cf. A023194, A066100, A001158.

%K nonn

%O 1,1

%A _Labos Elemer_, Aug 17 2001

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Last modified November 19 16:37 EST 2019. Contains 329323 sequences. (Running on oeis4.)