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A009087
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Numbers whose number of divisors is prime (i.e., numbers of the form p^(q-1) for primes p,q).
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22
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2, 3, 4, 5, 7, 9, 11, 13, 16, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239
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OFFSET
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1,1
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COMMENTS
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Invented by the HR Automatic Concept Formation Program. If the sum of divisors is prime, then the number of divisors is prime, i.e., this is a supersequence of A023194.
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REFERENCES
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S. Colton, Automated Theory Formation in Pure Mathematics. New York: Springer (2002)
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LINKS
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FORMULA
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p^(q-1), p, q primes.
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EXAMPLE
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tau(16)=5 and 5 is prime.
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MATHEMATICA
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Select[Range[250], PrimeQ[DivisorSigma[0, #]]&] (* Harvey P. Dale, Sep 28 2011 *)
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PROG
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(Haskell)
a009087 n = a009087_list !! (n-1)
a009087_list = filter ((== 1) . a010051 . (+ 1) . a100995) a000961_list
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CROSSREFS
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KEYWORD
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nice,nonn,easy
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AUTHOR
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Simon Colton (simonco(AT)cs.york.ac.uk)
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STATUS
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approved
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