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A009087
Numbers whose number of divisors is prime (i.e., numbers of the form p^(q-1) for primes p,q).
22
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
OFFSET
1,1
COMMENTS
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.
A010055(a(n)) * A010051(A100995(a(n))+1) = 1. - Reinhard Zumkeller, Jun 06 2013
REFERENCES
S. Colton, Automated Theory Formation in Pure Mathematics. New York: Springer (2002)
LINKS
Indranil Ghosh, Table of n, a(n) for n = 1..12546 (terms 1..1000 from T. D. Noe)
S. Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2, 1999, #2.
FORMULA
p^(q-1), p, q primes.
EXAMPLE
tau(16)=5 and 5 is prime.
MATHEMATICA
Select[Range[250], PrimeQ[DivisorSigma[0, #]]&] (* Harvey P. Dale, Sep 28 2011 *)
PROG
(Haskell)
a009087 n = a009087_list !! (n-1)
a009087_list = filter ((== 1) . a010051 . (+ 1) . a100995) a000961_list
-- Reinhard Zumkeller, Jun 05 2013
(PARI) is(n)=isprime(isprimepower(n)+1) \\ Charles R Greathouse IV, Sep 16 2015
CROSSREFS
Subsequence of A000961.
Sequence in context: A066724 A089237 A352870 * A026477 A079852 A084400
KEYWORD
nice,nonn,easy
AUTHOR
Simon Colton (simonco(AT)cs.york.ac.uk)
STATUS
approved