f←{({+/⍵=⍵∧⍳⍵}¨⍳2*⍵)⍳⍵}

> f 13
4096

> f 14
192

{.{.,{)1$%},,-=}+2@?,?}:f;

{.{)..,{)1$%},,-@=!}+do}:f;

13 f p  # => 4096
14 f p  # => 192
15 f p  # => 144

# Calculate numbers of divisors
#         .,{)1$%},,-
# Input stack: n
# After application: D(n)

.,          # push array [0 .. n-1] to stack
{           # filter array by function
  )         #   take array element and increase by one
  1$%      #   test division of n ($1) by this value
},          # -> List of numbers x where n is NOT divisible by x+1
,           # count these numbers. Stack now is n xd(n)
-           # subtracting from n yields the result



# Test if number of divisors D(n) is equal to d
#         {D=}+   , for D see above
# Input stack: n d
# After application: D(n)==d

{
           # swap stack -> d n
  D         # calculate D(n) -> d D(n)
  =         # compare
}+          # consumes d from stack and prepends it to code block



# Search for the first number which D(n) is equal to d
#         .T2@?,?    , for T see above
# Input stack: d
# After application: f(d)

.           # duplicate -> d d
T           # push code block (!) for T(n,d) -> d T(n,d)
2@?         # swap and calculate 2^d -> T(n,d) 2^d
,           # make array -> T(n,d) [0 .. 2^d-1]
?           # search first element in array where T(n,d) is true -> f(d)

f=lambda n,k=1:n==sum(k%i<1for i in range(1,k+1))and k or f(n,k+1)

def f(n,k=1):
    while 1:
        if sum(k%i<1for i in range(1,k+1))==n:return k
        k+=1

(For[i=1,DivisorSum[++i,1&]!=#,];i)&

(For[i=1,DivisorSum[++i,1&]!=#,];i)&@200

498960

f=.>:@]^:([~:[:*/[:>:_&q:@])^:_&1

   f 19
262144

f k=head[x|x<-[k..],length[y|y<-[1..x],mod x y==0]==k]

{{$[x=+/a=_a:y%!1+y;y;.z.s[x;1+y]]}[x;0]}

k){{$[x=+/a=_a:y%!1+y;y;.z.s[x;1+y]]}[x;0]}14
192
k){{$[x=+/a=_a:y%!1+y;y;.z.s[x;1+y]]}[x;0]}13
'stack

F n
i←0
l:i←i+1
→(n≠+/0=(⍳i)|i)/l
i

F 6
12

{⍵{⍺=+/0=⍵|⍨⍳⍵:⍵⋄⍺∇⍵+1}1}

f=function(N){n=1;while(N-sum(!n%%1:n))n=n+1;n}

f(6)
[1] 12
f(13)
[1] 4096

function f(N){for(j=i=m=1;m-N||j-i;j>i?i+=m=j=1:m+=!(i%++j));return i}

for(j=i=m=1;m-N||j-i;j>i?i+=m=j=1:m+=!(i%++j))

f n=until(i->n==sum[1|j<-[1..i],rem i j<1])(+1)1

i;f(n){while(n-g(++i));return i;}g(j){return j?!(i%j)+g(j-1):0;}

i;j;k;f(n){while(k-n&&++i)for(k=0,j=1;j<=i;k+=!(i%j++));return i;}

1<>p=[]
x<>p|mod x p>0=x<>(p+1)|1<2=(div x p<>p)++[p]
f k=product[p^(c-1)|(p,c)<-zip[r|r<-[2..k],2>length(r<>2)](k<>2)]

main=do putStrLn$show$ f (100000::Integer)

*Main> f 18
180
*Main> f 10000000
1740652905587144828469399739530000
*Main> f 1000000000
1302303070391975081724526582139502123033432810000
*Main> f 100000000000
25958180173643524088357042948368704203923121762667635047013610000
*Main> f 10000000000000
6558313786906640112489895663139340360110815128467528032775795115280724604138270000
*Main> f 1000000000000000
7348810968806203597063900192838925279090695601493714327649576583670128003853133061160889908724790000
*Main> f 100000000000000000
71188706857499485011467278407770542735616855123676504522039680180114830719677927305683781590828722891087523475746870000
*Main> f 10000000000000000000
2798178979166951451842528148175504903754628434958803670791683781551387366333345375422961774196997331643554372758635346791935929536819490000
*Main> f 10000000000000000000000
6628041919424064609742258499702994184911680129293140595567200404379028498804621325505764043845346230598649786731543414049417584746693323667614171464476224652223383190000

f(n,s){return--s?f(n,s)+!(n%s):1;}
x;
g(d){return++x,f(x,x)-d&&g(d),x;}

(For[k=1,DivisorSigma[0, k]!= #,k++]; k)&

(For[k = 1, DivisorSigma[0, k] != #, k++]; k) &[7]

(* 64 *)

smallestNumber[nDivisors_] :=
   Module[{k = 1},
   While[Length[Divisors[k]] != nDivisors, k++];k]

Table[{i, nDivisors[i]}, {i, 1, 20}] // Grid

2*RÆdi

2*RÆdi  Main link. Argument: n (integer)

2*      Compute 2**n.
  R     Range; yield [1, ..., 2**n]. Note that 2**(n-1) has n divisors, so this
        range contains the number we are searching for.
   Æd   Divisor count; compute the number of divisors of each integer in the range.
     i  Index; return the first (1-based) index of n.

int a(int d){int k=0,r,i;for(;r!=d;k++)for(i=2,r=1;i<=k;i++)if(!(k%i))r++;return k-1;}

from itertools import*
f=lambda n:next(i for i in count()if sum(1>i%(j+1)for j in range(i))==n)

fl

f     The list of factors of
      the input variable
 l    has length equal to
      the output variable.