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A066100
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Primes p such that their square p^2 has a sum of cube of divisors which is prime.
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4
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| It appears that squares of these primes give A063783, those numbers whose sum of cube of divisors is prime.
A simpler description: primes p such that p^6 + p^3 + 1 is prime. [From James Buddenhagen (jbuddenh(AT)gmail.com), Oct 10 2010]
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
| Divisor[3, p^2]=q, where both p and q are primes.
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EXAMPLE
| p=11: p^2=121, cube of divisors of p^2 ={p^6, p^3, 1}, sigma3[p^2]=p^6+p^3+1=1771561+1331+1=1772893=q, a prime.
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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)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Nov 13 2009]
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CROSSREFS
| Cf. A001158, A000040, A063783.
Sequence in context: A061482 A177854 A135161 * A029497 A109809 A096456
Adjacent sequences: A066097 A066098 A066099 * A066101 A066102 A066103
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Dec 04 2001
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