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%I #19 Jan 25 2021 20:49:44
%S 4,9,121,36481,72361,146689,259081,654481,683929,786769,1985281,
%T 2036329,3193369,3636649,3798601,4583881,5031049,5470921,5555449,
%U 6135529,6713281,7284601,7778521,16589329,20403289,21557449,22915369,26739241,27426169,30261001,30591961
%N Numbers k such that the sum of the cubes of divisors of k is a prime.
%H Harry J. Smith, <a href="/A063783/b063783.txt">Table of n, a(n) for n=1..1000</a>
%F Solutions to sigma_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 sigma_3(p^2) = p^6 + p^3 + 1 has polynomial of degree 6.
%e sigma_3(9) = 1 + 27 + 729 = 757 is 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. A001158, A023194, A066100.
%K nonn
%O 1,1
%A _Labos Elemer_, Aug 17 2001
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