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%I #33 Aug 30 2021 21:03:34
%S 1,4,16,64,36,1024,4096,144,65536,262144,576,4194304,1296,900,
%T 268435456,1073741824,9216,5184,68719476736,36864,1099511627776,
%U 4398046511104,3600,70368744177664,46656,589824,4503599627370496,82944
%N Smallest number with exactly 2n-1 divisors.
%C The terms are always squares (because the divisors of a nonsquare N come in pairs, d and N/d, and so their number is always even - _N. J. A. Sloane_, Dec 26 2018).
%H T. D. Noe, <a href="/A061283/b061283.txt">Table of n, a(n) for n = 1..1000</a> (using A005179)
%F a(n) = Min{k | A000005(k)=2n-1}.
%F a((p+1)/2) = 2^(p-1) for odd prime p. [Corrected by _Jianing Song_, Aug 30 2021]
%F From _Jianing Song_, Aug 30 2021: (Start)
%F a(n) = A016017(n)^2.
%F a(n) <= 2^(2n-2), where the equality holds if and only if n=1 or 2n-1 is prime. (End)
%e For n=15, a(15)=144 with 15 divisors: 1,2,3,4,6,8,9,12,16,18,24,36,48,72 and 144.
%t mp[1, m_] := {{}}; mp[n_, 1] := {{}}; mp[n_?PrimeQ, m_] := If[m < n, {}, {{n}}]; mp[n_, m_] := Join @@ Table[Map[Prepend[#, d] &, mp[n/d, d]], {d, Select[Rest[Divisors[n]], # <= m &]}]; mp[n_] := mp[n, n]; Table[mulpar = mp[2*n-1] - 1; Min[Table[Product[Prime[s]^mulpar[[j, s]], {s, 1, Length[mulpar[[j]]]}], {j, 1, Length[mulpar]}]], {n, 1, 100}] (* _Vaclav Kotesovec_, Apr 04 2021 *)
%Y Cf. A000005, A000290, A005408, A003680, A016017, A037992, A055079, A048691.
%Y Second bisection of A005179.
%K nonn
%O 1,2
%A _Labos Elemer_, May 22 2001
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