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A066100
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Primes p such that p^6 + p^3 + 1 is prime.
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5
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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FORMULA
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Primes p such that sigma_3(p^2) is prime.
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EXAMPLE
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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.
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MATHEMATICA
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Select[Prime@ Range@ 1200, PrimeQ@ DivisorSigma[3, #^2] &] (* Michael De Vlieger, Jul 16 2017 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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