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

%I A157450 #15 Jan 23 2025 00:21:33
%S A157450 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,
%T A157450 42,36,35,288,39,384,39,56,70,63,45,729,84,75,52,1024,56,1296,66,66,
%U A157450 128,1944,60,112,78,126,88,3072,78,140,78,150,224,5184,81,6144,256,104,90
%N A157450 a(n) = the n-th divisor of the smallest positive integer with exactly n^2 divisors.
%H A157450 Robert Israel, <a href="/A157450/b157450.txt">Table of n, a(n) for n = 1..5536</a>
%e A157450 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.
%p A157450 g:= proc(n, k) # lists of integers > k whose product is n
%p A157450       option remember;
%p A157450       local F, m;
%p A157450       if n = 1 then return [[]]
%p A157450       elif k >= n then return []
%p A157450       fi;
%p A157450       F:= select(`>`, numtheory:-divisors(n), k);
%p A157450       [seq(op(map(t -> [m, op(t)], procname(n/m, m-1))), m=F)]
%p A157450 end proc:
%p A157450 h:= proc(L) local i;
%p A157450      mul(ithprime(i)^(L[i]-1),i=1..nops(L))
%p A157450 end proc:
%p A157450 f:= proc(n) local C,x,D;
%p A157450    C:= map(sort,g(n^2,1),`>`);
%p A157450    x:= min(map(h,C));
%p A157450    D:= sort(convert(numtheory:-divisors(x),list));
%p A157450    D[n]
%p A157450 end proc:
%p A157450 map(f, [$1..70]); # _Robert Israel_, Jan 21 2025
%Y A157450 Cf. A061707.
%K A157450 nonn,look
%O A157450 1,2
%A A157450 _Leroy Quet_, Mar 01 2009
%E A157450 More terms from _R. J. Mathar_, Mar 14 2009
%E A157450 a(45)-a(64) from _Ray Chandler_, Jun 19 2009