A157450 a(n) = the n-th divisor of the smallest positive integer with exactly n^2 divisors.

1, 2, 3, 4, 6, 6, 9, 8, 10, 10, 24, 12, 32, 16, 18, 18, 64, 21, 81, 22, 28, 32, 144, 27, 40, 42, 36, 35, 288, 39, 384, 39, 56, 70, 63, 45, 729, 84, 75, 52, 1024, 56, 1296, 66, 66, 128, 1944, 60, 112, 78, 126, 88, 3072, 78, 140, 78, 150, 224, 5184, 81, 6144, 256, 104, 90

Offset: 1

Author

Leroy Quet, Mar 01 2009

Keywords

• nonn
• look

Examples

			The smallest positive integer with 5^2 divisors = A061707(5) = 1296. The first 5 of the 25 divisors of 1296 are: 1,2,3,4,6. Since the 5th divisor is 6, then a(5) = 6.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..5536

Crossrefs

Cf. A061707.

Programs

Maple

g:= proc(n, k) # lists of integers > k whose product is n
      option remember;
      local F, m;
      if n = 1 then return [[]]
      elif k >= n then return []
      fi;
      F:= select(`>`, numtheory:-divisors(n), k);
      [seq(op(map(t -> [m, op(t)], procname(n/m, m-1))), m=F)]
end proc:
h:= proc(L) local i;
     mul(ithprime(i)^(L[i]-1),i=1..nops(L))
end proc:
f:= proc(n) local C,x,D;
   C:= map(sort,g(n^2,1),`>`);
   x:= min(map(h,C));
   D:= sort(convert(numtheory:-divisors(x),list));
   D[n]
end proc:
map(f, [$1..70]); # Robert Israel, Jan 21 2025

Extensions

More terms from R. J. Mathar, Mar 14 2009

a(45)-a(64) from Ray Chandler, Jun 19 2009