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

2,1

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.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A000040, A002110, A027750.

Sequence in context: A325800 A037167 A267707 * A062431 A034351 A182737

Adjacent sequences: A221644 A221645 A221646 * A221648 A221649 A221650

Keyword

nonn

Author

Michel Lagneau, May 04 2013

Status

approved