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%I #17 Mar 12 2015 23:24:40
%S 3,10,28,66,234,204,456,828,1392,2232,2220,5904,7224,5640,9540,14160,
%T 14640,28140,25560,26280,79632,89640,64080,69840,181800,129780,134820,
%U 183120,189840,213360,495180,460320,934080,1001280,380520,1243440,1779960
%N Smallest number k such that prime(n) is the n-th divisor of k.
%C The similar problem "smallest number k such that prime(n) is the n-th prime divisor of k" is given by the sequence A002110: primorial numbers product of first n primes.
%H Donovan Johnson, <a href="/A221647/b221647.txt">Table of n, a(n) for n = 2..300</a>
%e a(6) = 234 because the divisors of 234 are {1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234}, and prime(6) = 13 is the 6th divisor of 234.
%p A221647 := proc(n)
%p local p,k,j ;
%p p := ithprime(n) ;
%p for j from 1 do
%p k := j*p ;
%p dvs := sort(convert(numtheory[divisors](k),list)) ;
%p if nops(dvs) >= n then
%p if op(n,dvs) = p then
%p return k ;
%p end if;
%p end if;
%p end do:
%p end proc:
%p seq(A221647(n),n=2..30) ; # _R. J. Mathar_, May 05 2013
%t nn = 20; t = Table[0, {nn}]; found = 1; n = 2; While[found < nn, n++; d = Divisors[n]; Do[If[i <= nn && d[[i]] == Prime[i] && t[[i]] == 0, t[[i]] = n; found++], {i, Length[d]}]]; Rest[t] (* _T. D. Noe_, May 07 2013 *)
%Y Cf. A000040, A002110, A027750.
%K nonn
%O 2,1
%A _Michel Lagneau_, May 04 2013
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