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A382492 a(n) is the least number that has exactly n 3-smooth divisors.

%I A382492 #12 Apr 26 2025 03:33:09
%S A382492 1,2,4,6,16,12,64,24,36,48,1024,72,4096,192,144,216,65536,288,262144,
%T A382492 432,576,3072,4194304,864,1296,12288,2304,1728,268435456,2592,
%U A382492 1073741824,3456,9216,196608,5184,6912,68719476736,786432,36864,10368,1099511627776,15552,4398046511104
%N A382492 a(n) is the least number that has exactly n 3-smooth divisors.
%C A382492 The record values occur at A046022.
%C A382492 All the terms are in A003586 and A025487.
%H A382492 Amiram Eldar, <a href="/A382492/b382492.txt">Table of n, a(n) for n = 1..3322</a>
%F A382492 a(n) = Min_{d|n} (2^(d-1)*3^(n/d-1)).
%F A382492 a(n) = 2^A382493(n) * 3^(n/(A382493(n)+1)-1).
%F A382492 a(p) = 2^(p-1) for prime p.
%F A382492 a(n) = A005179(n) if n is in A037143.
%t A382492 a[n_] := Min[Table[2^(d-1)*3^(n/d-1), {d, Divisors[n]}]]; Array[a, 60]
%o A382492 (PARI) a(n) = vecmin(apply(d -> 2^(d-1)*3^(n/d-1), divisors(n)));
%Y A382492 Cf. A003586, A005179, A025487, A037143, A046022, A072078, A382493.
%K A382492 nonn,easy
%O A382492 1,2
%A A382492 _Amiram Eldar_, Mar 29 2025