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A221647 Smallest number k such that prime(n) is the n-th divisor of k. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 20 05:51 EDT 2019. Contains 327212 sequences. (Running on oeis4.)