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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
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
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, May 04 2013
STATUS
approved