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A063783
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Sum of cube of divisors is prime.
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3
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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; internal format)
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OFFSET
| 1,1
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
| Solutions to DivisorSigma[3, x]=prime.
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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.
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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)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 31 2009]
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CROSSREFS
| Cf. A023194, A066100, A001158.
Sequence in context: A057136 A048411 A065379 * A168138 A128524 A027451
Adjacent sequences: A063780 A063781 A063782 * A063784 A063785 A063786
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Aug 17 2001
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