%I #10 Feb 26 2023 03:26:32
%S 1,4,36,720,25200,1940400,227026800,42454011600,10486140865200,
%T 3858899838393600,1902437620328044800,1120535758373218387200,
%U 953575930375608847507200,977415328634999068694880000,1218836914807843838662515360000,1775845384875028472931284879520000
%N a(n) is the least number that has exactly 2^n squarefree divisors and exactly 2^n powerful divisors.
%C a(n) is the least term k of A360902 with A034444(k) = A005361(k) = 2^n.
%H Amiram Eldar, <a href="/A360903/b360903.txt">Table of n, a(n) for n = 0..18</a>
%e a(1) = 4 since 4 is the least number that has 2^1 = 2 squarefree divisors (1 and 2) and 2 powerful divisors (1 and 4).
%e a(2) = 36 since 36 is the least number that has 2^2 = 4 squarefree divisors (1, 2, 3 and 6) and 4 powerful divisors (1, 4, 9 and 36).
%t f1[p_, e_] := 2; s1[1] = 1; s1[n_] := Times @@ f1 @@@ FactorInteger[n]; f2[p_, e_] := e; s2[1] = 1; s2[n_] := Times @@ f2 @@@ FactorInteger[n]; v = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]]; With[{m = 9}, seq = Table[0, {m}]; Do[If[(s = s1[v[[k]]]) == s2[v[[k]]], e = IntegerExponent[s, 2] + 1; If[e <= m && seq[[e]] == 0, seq[[e]] = v[[k]]]], {k, 1, Length[v]}]; seq]
%Y Subsequence of A025487 and A360902.
%Y Cf. A005361, A034444.
%K nonn
%O 0,2
%A _Amiram Eldar_, Feb 25 2023