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 A066100 Primes p such that p^6 + p^3 + 1 is prime. 4
 2, 3, 11, 191, 269, 383, 509, 809, 827, 887, 1409, 1427, 1787, 1907, 1949, 2141, 2243, 2339, 2357, 2477, 2591, 2699, 2789, 4073, 4517, 4643, 4787, 5171, 5237, 5501, 5531, 5693, 6311, 6329, 6359, 6911, 6947, 7019, 7253, 7349, 7499, 7577, 7691, 7907, 8819 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Original name: "Primes p such that the sum of the cubes of the divisors of p^2 is prime." It appears that squares of these primes give A063783, those numbers whose sum of cubes of divisors is prime. LINKS Harry J. Smith, Table of n, a(n) for n=1..1000 FORMULA Primes p such that sigma_3(p^2) is prime. EXAMPLE p=11: p^2=121, cubes of divisors of p^2 = {p^6, p^3, 1}, sigma_3(p^2) = p^6 + p^3 + 1 = 1771561 + 1331 + 1 = 1772893 = q, a prime. MATHEMATICA Select[Prime@ Range@ 1200, PrimeQ@ DivisorSigma[3, #^2] &] (* Michael De Vlieger, Jul 16 2017 *) PROG (PARI) { n=0; for (m=1, 10^9, p=prime(m); if (isprime(sigma(p^2, 3)), write("b066100.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Nov 13 2009 CROSSREFS Cf. A000040, A001158, A063783. Sequence in context: A177854 A273598 A135161 * A029497 A318130 A109809 Adjacent sequences:  A066097 A066098 A066099 * A066101 A066102 A066103 KEYWORD nonn AUTHOR Labos Elemer, Dec 04 2001 EXTENSIONS Name replaced with simpler description offered in an Oct 10 2010 comment by James R. Buddenhagen by Jon E. Schoenfield, Jul 17 2017 STATUS approved

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Last modified November 18 04:44 EST 2019. Contains 329248 sequences. (Running on oeis4.)