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Search: id:A066100
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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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3
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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; listen)
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OFFSET
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1,1
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COMMENT
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It appears that squares of these primes give A063783, those numbers whose sum of cube of divisors is prime.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
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Divisor[3, p^2]=q, where both p and q are primes.
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EXAMPLE
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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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PROGRAM
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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)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Nov 13 2009]
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CROSSREFS
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Cf. A001158, A000040, A063783.
Sequence in context: A042337 A061482 A135161 this_sequence A029497 A109809 A096456
Adjacent sequences: A066097 A066098 A066099 this_sequence A066101 A066102 A066103
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KEYWORD
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nonn,new
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Dec 04 2001
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