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 A063783 Sum of cube of divisors is prime. 4
 4, 9, 121, 36481, 72361, 146689, 259081, 654481, 683929, 786769, 1985281, 2036329, 3193369, 3636649, 3798601, 4583881, 5031049, 5470921, 5555449, 6135529, 6713281, 7284601, 7778521 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Harry J. Smith, Table of n, a(n) for n=1..1000 FORMULA Solutions to DivisorSigma[3, x]=prime. EXAMPLE 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. sigma[3,9]=1+27+729=757, a prime. MATHEMATICA Select[Prime[Range[500]]^2, PrimeQ@ DivisorSigma[3, #] &] (* Michael De Vlieger, Jul 16 2017 *) PROG (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 CROSSREFS Cf. A023194, A066100, A001158. Sequence in context: A048411 A225739 A065379 * A168138 A267898 A324981 Adjacent sequences:  A063780 A063781 A063782 * A063784 A063785 A063786 KEYWORD nonn AUTHOR Labos Elemer, Aug 17 2001 STATUS approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)