cp's OEIS Frontend

A221647 Smallest number k such that prime(n) is the n-th divisor of k.

%I A221647 #23 May 28 2025 09:35:01
%S A221647 3,10,28,66,234,204,456,828,1392,2232,2220,5904,7224,5640,9540,14160,
%T A221647 14640,28140,25560,26280,79632,89640,64080,69840,181800,129780,134820,
%U A221647 183120,189840,213360,495180,460320,934080,1001280,380520,1243440,1779960
%N A221647 Smallest number k such that prime(n) is the n-th divisor of k.
%C A221647 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 A221647 Donovan Johnson, <a href="/A221647/b221647.txt">Table of n, a(n) for n = 2..300</a>
%e A221647 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 A221647 := proc(n)
%p A221647         local p,k,j ;
%p A221647         p := ithprime(n) ;
%p A221647         for j from 1 do
%p A221647                 k := j*p ;
%p A221647                 dvs := sort(convert(numtheory[divisors](k),list)) ;
%p A221647                 if nops(dvs) >= n then
%p A221647                 if op(n,dvs) = p then
%p A221647                         return k ;
%p A221647                 end if;
%p A221647                 end if;
%p A221647         end do:
%p A221647 end proc:
%p A221647 seq(A221647(n),n=2..30) ; # _R. J. Mathar_, May 05 2013
%t A221647 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 *)
%o A221647 (PARI) a(n) = my(k=2, f=factor(k), p=prime(n)); while ((numdiv(f)<n) || (divisors(f)[n] != p), k++; f=factor(k)); k; \\ _Michel Marcus_, May 28 2025
%Y A221647 Cf. A000040, A002110, A027750.
%Y A221647 Sequences giving smallest number whose n-th divisor satisfies other conditions: A087134 (prime), A119311 (prime power), A119312 (squarefree), A226101 (multiple of n-th prime), A256605 (is n+1), A383402 (largest odd divisor).
%K A221647 nonn
%O A221647 2,1
%A A221647 _Michel Lagneau_, May 04 2013