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

3, 10, 28, 66, 234, 204, 456, 828, 1392, 2232, 2220, 5904, 7224, 5640, 9540, 14160, 14640, 28140, 25560, 26280, 79632, 89640, 64080, 69840, 181800, 129780, 134820, 183120, 189840, 213360, 495180, 460320, 934080, 1001280, 380520, 1243440, 1779960

Offset: 2

Author

Michel Lagneau, May 04 2013

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 2..300

Crossrefs

Cf. A000040, A002110, A027750.

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).

Programs

Maple

A221647 := proc(n)
        local p,k,j ;
        p := ithprime(n) ;
        for j from 1 do
                k := j*p ;
                dvs := sort(convert(numtheory[divisors](k),list)) ;
                if nops(dvs) >= n then
                if op(n,dvs) = p then
                        return k ;
                end if;
                end if;
        end do:
end proc:
seq(A221647(n),n=2..30) ; # R. J. Mathar, May 05 2013

Mathematica

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 *)

PARI

a(n) = my(k=2, f=factor(k), p=prime(n)); while ((numdiv(f)Michel Marcus, May 28 2025