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%I #13 Jan 02 2021 04:50:16
%S 1,4,16,36,65536,144,18446744073709551616,576,1296,589824
%N a(n) is the least number with exactly n exponential divisors.
%C a(11) = 2^(2^10) has 309 digits and is too large to be included in the data section.
%C See the link for more values of this sequence.
%H Amiram Eldar, <a href="/A340233/b340233.txt">Table of n, a(n) for n = 1..12</a>
%H Amiram Eldar, <a href="/A340233/a340233.txt">Table of n, a(n) for n = 1..100</a> (given by prime factorizations)
%F A049419(a(n)) = n and A049419(k) != n for all k < a(n).
%e a(2) = 4 since 4 is the least number with 2 exponential divisors, 2 and 4.
%t f[p_, e_] := DivisorSigma[0, e]; d[1] = 1; d[n_] := Times @@ (f @@@ FactorInteger[n]); max = 6; s = Table[0, {max}]; c = 0; n = 1; While[c < max, i = d[n]; If[i <= max && s[[i]] == 0, c++; s[[i]] = n]; n++]; s (* ineffective for n > 6 *)
%Y Subsequence of A025487.
%Y Cf. A049419, A318278, A322791.
%Y Similar sequences: A005179 (all divisors), A038547 (odd divisors), A085629 (coreful divisors), A309181 (nonunitary), A340232 (bi-unitary).
%K nonn
%O 1,2
%A _Amiram Eldar_, Jan 01 2021
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