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%I #36 Jun 18 2021 21:57:03
%S 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,
%T 71,73,79,81,83,89,97,101,103,107,109,113,121,127,131,137,139,149,151,
%U 157,163,167,169,173,179,181,191,193,197,199,211,223,227,229,233,239
%N Numbers whose number of divisors is prime (i.e., numbers of the form p^(q-1) for primes p,q).
%C 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.
%C A010055(a(n)) * A010051(A100995(a(n))+1) = 1. - _Reinhard Zumkeller_, Jun 06 2013
%D S. Colton, Automated Theory Formation in Pure Mathematics. New York: Springer (2002)
%H Indranil Ghosh, <a href="/A009087/b009087.txt">Table of n, a(n) for n = 1..12546</a> (terms 1..1000 from T. D. Noe)
%H S. Colton, <a href="http://www.cs.uwaterloo.ca/journals/JIS/colton/joisol.html">Refactorable Numbers - A Machine Invention</a>, J. Integer Sequences, Vol. 2, 1999, #2.
%F p^(q-1), p, q primes.
%e tau(16)=5 and 5 is prime.
%t Select[Range[250],PrimeQ[DivisorSigma[0,#]]&] (* _Harvey P. Dale_, Sep 28 2011 *)
%o (Haskell)
%o a009087 n = a009087_list !! (n-1)
%o a009087_list = filter ((== 1) . a010051 . (+ 1) . a100995) a000961_list
%o -- _Reinhard Zumkeller_, Jun 05 2013
%o (PARI) is(n)=isprime(isprimepower(n)+1) \\ _Charles R Greathouse IV_, Sep 16 2015
%Y Subsequence of A000961.
%Y Cf. A023194, A036454, A203967.
%K nice,nonn,easy
%O 1,1
%A Simon Colton (simonco(AT)cs.york.ac.uk)