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%I #7 Jul 23 2024 20:47:27
%S 1,4,12,36,72,144,288,576,720,1728,4608,2880,18432,7200,8640,14400,
%T 294912,20160,1179648,43200,50400,115200,18874368,100800,172800,
%U 460800,181440,352800,1207959552,302400,4831838208,705600,806400,7372800,1058400,907200,309237645312
%N a(n) is the least number whose divisors have a mean number of divisors that equals n.
%C a(n) is the least number k such that A374902(k)/A374903(k) = A007425(k)/A000005(k) = n.
%C All the terms are in A025487.
%H Amiram Eldar, <a href="/A374906/b374906.txt">Table of n, a(n) for n = 1..1000</a>
%F a(p) = 9 * 2^(p-2) for prime p >= 5.
%F a(p^e) = 9 * 2^(p^e-2) for prime p >= 3 and e >= 2.
%t lps = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]]; f[p_, e_] := e/2 + 1; f[1] = 1; f[n_] := Times @@ f @@@ FactorInteger[n]; s = f /@ lps; lps[[TakeWhile[Flatten[FirstPosition[s, #] & /@ Range[Max[s]]], ! MissingQ[#] &]]]
%Y Cf. A000005, A005179, A007425, A025487, A374902, A374903, A374904, A374905, A374907.
%K nonn
%O 1,2
%A _Amiram Eldar_, Jul 23 2024